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# Good books in Modular Representation Theory

Hi every one!

I am reading some paper and it uses Modular Representation Theory. I even dont really know about Representation Theory and I am looking for a good book for beginner. Could you please give me some suggestion for beginning Modular Representation Theory?

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Everyone seems to be assuming that you mean modular representations of finite groups. There are other kinds of modular representation theory: can you be more specific? – Sheikraisinrollbank Feb 19 '11 at 16:17
I would also recommend Navarro's book and the book by Collins. – Steve D Feb 20 '11 at 3:37

If I understand you correctly, you're saying that you're not familar with ordinary (ie char $0$) representation theory. If this is correct, then you'll find books on modular representation theory tough going. I recommend starting with Serre's short book "Linear representations of finite groups". The first 2 sections are a very elegant and efficient treatment of the char $0$ theory, and the last section is a nice start on the char $p$ theory. After that, you'll be much better prepared for one of the other books people mention (and I'll second Alperin's "Local representation theory").

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The question strikes me as too vague (what is that paper you're reading, by the way?). Like others, I'm assuming the subject is finite groups, rather than algebraic groups or quantum groups or something connected with modular forms. Usually the modular theory of finite groups is approached via the classical Frobenius-Schur theory, which is especially slanted toward characters but can be recast in terms of the Wedderburn structure theory of group algebras. Modular theory allows for a wide variety of approaches, including the narrow but fruitful one in Alperin's book. Serre's concise book starts out in a fairly elementary style (for an audience of chemists), but by the third part on modular representations the sophistication has escalated a lot. It's an important short treatment but scary for newcomers.

There's a lot to be said for the somewhat old-fashioned, concrete approach taken in the original Curtis & Reiner book Representations of Finite Groups and Associative Algebras, toward the end of the book. It does presuppose some of the earlier material, slanted toward ring theory rather than characters.

For a really short and relatively elementary expository treatment of both "ordinary" (characteristic 0) and modular representation theory, motivated by a single family of almost-simple groups, there's an old paper of mine in American Mathematican Monthly (1975), "Representations of $SL(2,p)$".

The bottom line is that you need to focus on which specific area of representation theory is essential for your needs. It's a very big subject.

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Hi, a very elementary written book is Local Representation Theory by Alperin.The second book on finite groups by Huppert has also a big part about modular representation theory.(you should read the first book too,with an long introduction to representation theory in the semisimple case) a more advanced book is that of feit and a recent (2010) book is "Representations of Groups: A Computational Approach" by Lux and Pahlings.It has many nice examples with gap and the sporadic groups.You should also take a look for the books of curtis and reiner.The one from 1962 is easy to read and might be the best introduction.

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How can a book be very hard to read "since it covers many other topics"? You must be hiding the real reason. – darij grinberg Feb 19 '11 at 16:04
Ok,that sounds strange so i changed that.I dont know how to explain.Maybe just try to read it. – trew Feb 19 '11 at 16:08
Alperin's book is not just "elementary written", it's beautifully written. – Chris Godsil Feb 19 '11 at 16:14
But one has to say that Alperin covers only a small part of modular representation theory, in particular block theory. There is nothing about decomposition theory. Also everything is written in the language of modules, but some results become more clearer if expressed for example in terms of central idempotents. After reading Alperin's book for example you may have a hard time understanding what Brauers main theorems as listed on wikipedia have to do with the three theorems you learned from Alperin... – Johannes Hahn Feb 19 '11 at 16:52

David Benson: Modular Representation Theory. New Trends and Methods. Lecture Notes in Mathematics 1081, 1984 (2nd print 2006)

is also a good book on the topic.

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Daniel Bump's "Automorphic forms and representations" is pretty nice if by your question you mean something about modular forms and representation theory.

I agree with J.Humphreys that your question isn't specific enough...

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The slopes R package calculates the slope (longitudinal steepness, also known as gradient) of roads, rivers and other linear (simple) features, based on two main inputs:

Data on slopes are useful in many fields of research, including hydrology, natural hazards (including flooding and landslide risk management), recreational and competitive sports such as cycling, hiking, and skiing. Slopes are also also important in some branches of transport and emissions modelling and ecology. See the intro-to-slopes vignette for details on fields using slope data and the need for this package.

This README covers installation and basic usage. For more information about slopes and how to use the package to calculate them, see the get started and the introducion to slopes vignette.

## How it works

The package takes two main types of input data for slope calculation: - vector geographic objects representing linear features, and - elevation values from a digital elevation model representing a continuous terrain surface or which can be downloaded using functionality in the package

The package can be used with two sources of elevation data: - openly available elevation data via an interface to the ceramic package, enabling estimation of hilliness for routes anywhere worldwide even when local elevation data is lacking. The package takes geographic lines objects and returns elevation data per vertex (providing the output as a 3D point geometry in the sf package by default) and per line feature (providing average gradient by default). - an elevation model, available on your machine.

## Getting started

### Installation

Install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("ropensci/slopes")

If you do not already have DEM data and want to make use of the package’s ability to download them using the ceramic package, install the package with suggested dependencies, as follows:

# install.packages("remotes")
remotes::install_github("ropensci/slopes", dependencies = "Suggests")

Furthermore, you will need to add a MapBox API key to be able to get DEM datasets, by signing up and registering for a key at https://account.mapbox.com/access-tokens/ and then following these steps:

usethis::edit_r_environ()
MAPBOX_API_KEY=xxxxx # replace XXX with your api key

## Basic examples

Load the package in the usual way. We will also load the sf library:

library(slopes)
library(sf)

The minimum input data requirement for using the package is an sf object containing LINESTRING geometries, as illustrated below (requires a MapBox API key):

sf_linestring = lisbon_route # import or load a linestring object
sf_linestring_xyz = elevation_add(sf_linestring)  # dem = NULL
#> https://api.mapbox.com/v4/mapbox.terrain-rgb/

With the default argument dem = NULL, the function downloads the necessary elevation information from Mapbox. You can also this use a local digital elevation model (dem = ...), as shown in the example below:

sf_linestring_xyz_local = elevation_add(sf_linestring, dem = dem_lisbon_raster)
#> Loading required package: sp

In both cases you can obtain the average gradient of the linestring with slope_xyz() and plot the elevation profile with plot_slope() as follows:

slope_xyz(sf_linestring_xyz_local)
#>          1
#> 0.07817098
plot_slope(sf_linestring_xyz_local)

See more functions in Get started vignette.

## Code of Conduct

slopes package is released under the Contributor Code of Conduct of rOpenSci. By contributing to this project, you agree to abide by its terms.

format: plain


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# I need compute a rational limit that involves roots

I need compute the result of this limit without l'hopital's rule, I tried different techniques but I did not get the limit, which is 1/32, I would appreciate if somebody help me. Thanks.

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$

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Write $x = \sqrt[5]{y}$. Look sharp. Simplify. –  Daniel Fischer Aug 19 '14 at 23:01
Let $x = y^{1/5}$ and then this is equivalent to $\lim_{x \rightarrow 2} \frac{x^2 - 3x +2}{x^5 - 4x^3} = \lim \frac{2x-3}{5x^4 - 12x^2} = \frac{1}{32}$. –  Chris K Aug 19 '14 at 23:03
@ChrisK Thank you for your help, i like your technique :) –  egarro Aug 19 '14 at 23:06
@ChrisK How do you get that x^2-3x+2 is equal to 2x -3 and x^5 -4x^3 is 5x^4 -12x^2? –  egarro Aug 19 '14 at 23:10
@egarro, they are not equal. Note that $(x^2-3x+2)' = 2x-3$ and the other case is similar. This is an application of l'Hopital's rule; I missed not using it. See the other answers for an alternative method. –  Chris K Aug 20 '14 at 2:48

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$

We set $y^{\frac{1}{5}}=x$

When $y \to 32, x \to 2$

So,we have:

$$\lim_{x \to 2} \frac{x^2-3x+2}{x^5-4x^3}=\lim_{x \to 2} \frac{(x-1) (x-2)}{x^3(x^2-4)}=\lim_{x \to 2} \frac{(x-1)(x-2)}{x^3(x-2)(x+2)}=\lim_{x \to 2} \frac{x-1}{x^3(x+2)}=\frac{1}{8 \cdot 4}=\frac{1}{32}$$

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Thank you so much! –  egarro Aug 19 '14 at 23:11

$$\lim_{y\to32}\frac{\sqrt[5]{y^2} - 3\sqrt[5]{y} + 2}{y - 4\sqrt[5]{y^3}}$$ taking $\sqrt[5]{y}=x$ we have that $$\lim_{x\to2}\frac{x^2-3x+2}{x^5-4x^3}=\lim_{x\to2}\frac{x^2-x-2x+2}{x^3(x^2-4)}=$$ $$=\lim_{x\to2}\frac{x(x-1)-2(x-1)}{x^3(x-2)(x+2)}=\lim_{x\to2}\frac{(x-1)(x-2)}{x^3(x-2)(x+2)}$$ $$=\lim_{x\to2}\frac{(x-1)}{x^3(x+2)}=1/32$$

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Thanks for your help. –  egarro Aug 19 '14 at 23:14


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# Difference between revisions of "Euclidean domain"

A Euclidean domain (or Euclidean ring) is a type of ring in which the Euclidean algorithm can be used.

Formally we say that a ring $R$ is a Euclidean domain if:

• It is an integral domain.
• There a function $N:R\setminus\{0\}\to \mathbb Z_{\ge0}$ called a Norm such that for all nonzero $a,b\in R$ there are $q,r\in R$ such that $a = bq+r$ and either $N(r) or $r=0$.

Some common examples of Euclidean domains are:

• The ring of integers $\mathbb Z$ with norm given by $N(a) = |a|$.
• The ring of Gaussian integers $\mathbb Z[i]$ with norm given by $N(a+bi) = a^2+b^2$.
• The ring of polynomials $F[x]$ over any field $F$ with norm given by $N(p) = \deg p$.


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# MarkovProcess¶

class probnum.randprocs.markov.MarkovProcess(initarg, initrv, transition)

Random processes with the Markov property.

A Markov process is a random process with the additional property that conditioned on the present state of the system its future and past states are independent. This is known as the Markov property or as the process being memoryless. A Markov process can be fully defined via an initial state and a state transition.

Parameters

RandomProcess

Random processes.

GaussianProcess

Gaussian processes.

Attributes Summary

 dtype Data type of (elements of) the random process evaluated at an input. input_dim Shape of inputs to the random process. output_dim Shape of the random process evaluated at an input.

Methods Summary

 __call__(args) Evaluate the random process at a set of input arguments. cov(args0[, args1]) Covariance function or kernel. marginal(args) Batch of random variables defining the marginal distributions at the inputs. mean(args) Mean function. push_forward(args, base_measure, sample) Transform samples from a base measure into samples from the random process. sample(rng[, args, size]) Sample paths from the random process. std(args) Standard deviation function. var(args) Variance function.

Attributes Documentation

dtype

Data type of (elements of) the random process evaluated at an input.

Return type

dtype

input_dim

Shape of inputs to the random process.

Return type

int

output_dim

Shape of the random process evaluated at an input.

Return type

int

Methods Documentation

__call__(args)[source]

Evaluate the random process at a set of input arguments.

Parameters

args (Union[floating, ndarray]) – shape=(input_dim,) or (n, input_dim) – Input(s) to evaluate random process at.

Returns

shape=(), (output_dim,) or (n, output_dim) – Random process evaluated at the inputs.

Return type

randvars.RandomVariable

cov(args0, args1=None)[source]

Covariance function or kernel.

Returns the covariance function $$\operatorname{Cov}(f(x_0), f(x_1)) = \mathbb{E}[(f(x_0) - \mathbb{E}[f(x_0)])(f(x_0) - \mathbb{E}[f( x_0)])^\top]$$ of the process evaluated at $$x_0$$ and $$x_1$$. If only args0 is given the covariance among the components of the random process at the inputs defined by args0 is computed.

Parameters
Returns

shape=(), (output_dim, output_dim), (n0, n1) or (n0, n1, output_dim, output_dim) – Covariance of the process at args0 and args1. If only args0 is given the kernel matrix $$K=k(x_0, x_0)$$ is computed.

Return type

_OutputType

marginal(args)

Batch of random variables defining the marginal distributions at the inputs.

Parameters

args (~InputType) – shape=(input_dim,) or (n, input_dim) – Input(s) to evaluate random process at.

Return type

_RandomVariableList

mean(args)[source]

Mean function.

Returns the mean function evaluated at the given input(s).

Parameters

args (Union[floating, ndarray]) – shape=(input_dim,) or (n, input_dim) – Input(s) where the mean function is evaluated.

Returns

shape=(), (output_dim, ) or (n, output_dim) – Mean function of the process evaluated at inputs x.

Return type

_OutputType

push_forward(args, base_measure, sample)[source]

Transform samples from a base measure into samples from the random process.

This function can be used to control sampling from the random process by explicitly passing samples from a base measure evaluated at the input arguments.

Parameters
Return type

ndarray

sample(rng, args=None, size=())

Sample paths from the random process.

If no inputs are provided this function returns sample paths which are callables, otherwise random variables corresponding to the input locations are returned.

Parameters
Return type

Union[Callable[[~InputType], ~OutputType], ~OutputType]

std(args)

Standard deviation function.

Parameters

args (~InputType) – shape=(input_dim,) or (n, input_dim) – Input(s) to the standard deviation function.

Returns

shape=(), (output_dim,) or (n, output_dim) – Standard deviation of the process at args.

Return type

_OutputType

var(args)

Variance function.

Returns the variance function which is the value of the covariance or kernel evaluated elementwise at args for each output dimension separately.

Parameters

args (~InputType) – shape=(input_dim,) or (n, input_dim) – Input(s) to the variance function.

Returns

shape=(), (output_dim,) or (n, output_dim) – Variance of the process at args.

Return type

_OutputType


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This can be a very attention-grabbing and great publication. It offers a transparent and deep advent approximately advanced geometry, particularly the examine of complicated manifolds. those are differentiable manifolds endowed with the extra datum of a fancy constitution that's extra inflexible than the geometrical constructions utilized in differential geometry. advanced geometry is at the crossroad of algebraic and differential geometry. advanced geometry can also be changing into a stimulating and useful gizmo for theoretical physicists operating in string thought and conformal box conception. The physicist, can be very comfortable to find the interaction among advanced geometry and supersymmetry and replicate symmetry.

The publication starts off by means of explaining the neighborhood thought and all you must comprehend the worldwide constitution of complicated manifolds. Then we get an creation to the complicated manifolds as such, the place the reader can gradually understand the variation among genuine manifolds and intricate ones. Then he will get an account of the speculation of Kälher manifolds. And the physicist might be blissful to discover therein a primary step at the street going from complicated geometry to conformal box concept and supersymmetry. One bankruptcy is devoted to the learn of holomorphic vector bundles (connections, curvature, Chern classes). during this context, the reader will make clear the family members among Riemannian and Kälher geometries. With all these items it's then attainable to target a few purposes of cohomology. This ends up in a pleasant advent to the recognized Hirzebruch-Riemann-Roch theorem and to Kodaira vanishing and embedding theorems. The final bankruptcy of the ebook tackles the extremely important issues of deformations of advanced structures.

This bankruptcy could be attention-grabbing specially for readers which are learning Calabi-Yau manifolds and reflect symmetries. the most textual content of the e-book is done through pedagogical appendices. One approximately Hodge thought and the opposite approximately sheaf cohomology.

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Inside of cognitive technological know-how, methods at present dominate the matter of modeling representations. The symbolic strategy perspectives cognition as computation related to symbolic manipulation. Connectionism, a unique case of associationism, versions institutions utilizing synthetic neuron networks. Peter Gardenfors bargains his thought of conceptual representations as a bridge among the symbolic and connectionist techniques.

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There's an basically “tinker-toy” version of a trivial package over the classical Teichmüller area of a punctured floor, known as the embellished Teichmüller area, the place the fiber over some extent is the gap of all tuples of horocycles, one approximately each one puncture. This version results in an extension of the classical mapping type teams known as the Ptolemy groupoids and to yes matrix types fixing similar enumerative difficulties, every one of which has proved helpful either in arithmetic and in theoretical physics.

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The authors turn out a few subtle asymptotic estimates for optimistic blow-up suggestions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a soft bounded area of $\mathbb{R}^n$, $n\geq 3$. particularly, they convey that focus can happen merely on boundary issues with nonpositive suggest curvature whilst $n=3$ or $n\geq 7$.

Additional info for Complex Geometry: An Introduction (Universitext)

Sample text

1 (k- 2 ) ( k-1) £! Ln + 1 - k - C l1 bk-2), £ = j, j + 1 *1££1 /k - 2 = ( - 1) 2 (n + 1 - k - £) ! 1 k( \- 1) j! L n- k -1 1 1 ((3'k(-' l1) * 1 L1(3' 1 k(-' )1 = (- 1) (n k j) ! 1 _ _ · This yields k(k+tl ( - 1) _2 _ (n - k - j) ! 1 J. * Va = (n - k - j)(L� - k -J )1 1 (rk)) 0 w - (j + 1)(L� - k -J 1 1 (/k - 2)) 0 w - (L� - k -j11 (f3� - 1 )) 0 * 2(x 1 ) - (L� - k -J1 1 (f3�-d) 0 *2(Y 1 ) +L� - k -J 1 1 (rk) - L� + 1 - k - J I1 bk - 2) On the other hand, Ln - k -j l( a) = L� - k - j 1 1 (rk ) + (n - k - j) (L� - k - j - 1 1 1 (/k )) 0 w + (L� - k -J+ 1 1 1 bk - 2) + (n - k - j)(L� - k -J idrk - 2)) 0 w + (L� - k -J I1 ((3� _ 1 )) 0 ( -y 1 ) + (L� - k -jl1 (f3L 1 )) 0 x 1 + (k - n - 1)(L� - k -J I1 bk - 2)) 0 w Comparing both expressions yields the result.

Thus, X = X n Z(fi ) for i = 1 or i = 2. Hence, at least one of the functions h or h vanishes on X and, therefore, is contained in the ideal I(X) . Conversely, let I(X) be a prime ideal and let X = X 1 u X2 with Xi analytic. If fi E I(Xi ), i = 1 , 2, then h · h E I(X). Hence, h E I(X) or h E I(X). Thus, it suffices to show that if X i- X 1 and X i- X2 , then there exist elements h E I(XI ) \ I(X) and h E I(X2 ) \ I(X). This follows 0 immediately from Lemma 1 . 26. Lemma 1 . 28 also shows that for f E Ocn,o the zero set Z(f) is irreducible if and only if there exists an irreducible g E Ocn,o such that f = g k for some k.

7 the function ��� = fr on Bek C C. Moreover, the function 9I is holomorphic in Zk+1 , . . , Zn and differentiable in the other variables. Set 1 := ( 1 )� L k I 9J�ZJ \ { k } · Then 8n(z) = 0 for i > k and 8k /(z) = -a 1 . Hence, a + 81 is still a-closed, but it does not involve any dzi for i � k satisfies - E 0 anymore. Then one concludes by induction. e. In the following, B shall denote a polydisc E i = oo is allowed. 9 ( 8-Poincare lemma on the open disc) If a E Ap , q (B) is 8-closed and q > 0, then there exists f3 E Ap,q- 1 (B) with a = 8{3.


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• ### A Study of Shell Model Neutron States in $^{207,209}Pb$ Using the Generalized Woods-Saxon plus Spin-Orbit Potential(1506.04055)

July 11, 2016 nucl-th
The experimental binding energies of single-particle and single-hole neutron states belonging to neutron shells that extend from N = 126 to 184 and 82 to 126 respectively, have been reproduced by solving the Schr\"{o}dinger equation with a potential that has two components: the generalized Woods-Saxon (GWS) potential and the spin-orbit (SO) coupling term. The GWS potential contains the traditional WS potential plus a term (SU) whose intensity reaches a maximum in the nuclear surface. Our results indicate the existence of a explicit relationship between the strength of the SU potential and the orbital angular momentum quantum number $\ell$ of the state. This dependence has been used to make reasonable predictions for the excitation energy centroids of states located inside and outside the neutron shells investigated. Comparisons are made with results reported in previous investigations.
• ### Single Particle Strengths and Mirror States in $^{15}$N$-^{15}$O below 12.0 MeV(1407.4140)

July 15, 2014 nucl-ex
New $^{14}$N(d,p) angular distribution data were taken at a deuteron bombarding energy of 16 MeV to locate all narrow single particle neutron states up to 15 MeV in excitation. A new shell model calculation is able to reproduce all levels in $^{15}$N up to 11.5 MeV and is used to characterize a narrow single particle level at 11.236 MeV and to provide a map of the single particle strengths. The known levels in $^{15}$N are then used to determine their mirrors in the lesser known nucleus $^{15}$O. The 2s$_{1/2}$ and 1d$_{5/2}$ single particle centroid energies are determined for the $^{15}$N$-^{15}$O mirror pair as: $^{15}$N $(\text{2s}_{1/2}) = 8.08$ MeV, $^{15}$O $(\text{2s}_{1/2}) = 7.43$ MeV, $^{15}$N $(\text{1d}_{5/2}) = 7.97$ MeV, and $^{15}$O $(\text{1d}_{5/2}) = 7.47$ MeV. These results confirm the degeneracy of these orbits and that the $^{15}$N$-^{15}$O nuclei are where the transition between the $\text{2s}_{1/2}$ lying below the $\text{1d}_{5/2}$ to lying above it, takes place. The $\text{1d}_{3/2}$ single particle strength is estimated to be centered around 13 MeV in these nuclei.


text:
Intro to Moment of Inertia Video Lessons

Concept

# Problem: A 2.2 kg, 20-cm-diameter turntable rotates at 80 rpm on frictionless bearings. Two 600 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rpm, just after this event?

###### FREE Expert Solution

From the conservation of angular momentum, the momentum before the event is equal to the momentum after the event.

$\overline{){{\mathbf{I}}}_{{\mathbf{i}}}{{\mathbf{\omega }}}_{{\mathbf{i}}}{\mathbf{=}}{{\mathbf{I}}}_{{\mathbf{f}}}{{\mathbf{\omega }}}_{{\mathbf{f}}}}$

The initial moment of inertia,

Ii = (1/2)Mr2

Radius, r = 20/2 = 10 cm

Ii = (1/2)(2.2)(10 × 10-2)2 = 0.011 kg•m2

85% (136 ratings)
###### Problem Details

A 2.2 kg, 20-cm-diameter turntable rotates at 80 rpm on frictionless bearings. Two 600 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diagonal, and stick. What is the turntable's angular velocity, in rpm, just after this event?


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# Bordered table: weird last row?

I am trying to make a simple table in LaTeX following some tutorials but I am getting an extra column/row after the last row? Why is this? Any help would be highly appreciated :)

\documentclass[]{article}

\begin{document}

\title{Title}
\author{Author}
\date{\today}
\maketitle

\begin{center}
\begin{tabular}{| c | c | c | c |} \hline
Date & Reasons for review & Changes & Version \\ \hline
yy/xx/2012 & First edition & - & 1.0 \\ \hline
yy/xx/2012 & Something added & Section 5 & 1.01 \\ \hline
￼￼￼￼yy/xx/2012 & More things & Section n & 1.02 \\ \hline
￼￼\end{tabular}
\end{center}

\end{document}

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You've got some extra white space in the last row. Remove the white space in front of \end{tabular} and you'll be set. – A.Ellett Jan 4 '13 at 2:02
Thanks! Could you put this as an answer? :) So I can put the check mark – nacho4d Jan 4 '13 at 2:05
How does one end up with OBJECT REPLACEMENT CHARACTER in their source? (It’s twice in front of \end{tabular} and four times in front of the actual last row.) – Qrrbrbirlbel Jan 4 '13 at 2:15
@Qrrbrbirlbel, how'd you figure out what that character was? I only knew it wasn't ascii. – A.Ellett Jan 4 '13 at 2:19
@A.Ellett copy/paste worked for me :) – percusse Jan 4 '13 at 2:35


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Introduction to Linear Algebra for Applied Machine Learning with Python 425 points by Anon84 3 months ago | hide | past | favorite | 52 comments

 Hi, I did that article :)https://twitter.com/CodeBug88Saludos
 Is the 'sente' in your GitHub handle the opposite of 'gote', or something else entirely?
 Oh yes, I used to play a lot of Go/Baduk :)
 Ola
 I like that this touches on some of the algebra aspects. I always find it strange when I see something about “linear algebra” that never mentions linear maps, vector spaces or bases. Perhaps the mechanics of computing with matrices is better for an introduction for people who are only interested in machine learning but the mathematician in me feels like it is important to get across that in some specific sense the numbers in a matrix are arbitrary and that the essence of the thing is simpler.I’m a bit surprised that this doesn’t mention suffix notation, especially as multilinear maps are so common in machine learning and suffix notation is such a good way to work with them.
 I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book.I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linear Algebra later and write a comparison.
 Jim Hefferon, who is also a HN member, has a great free Linear Algebra textbook. People all have their own preferences but I actually prefer his to Strang's.
 +1 for Heffron's book, which was posted here 2 weeks ago [0]. He also published all the solutions to the exercises! [1]
 As a heads up, the Boyd book is available free on his website.
 My sense is that Vandenberghe is great for getting your feet wet and building intuition, but it's not as deep as Strang in its coverage and has fewer problems. Definitely still worth reading through especially since the problems lend themselves well to working through with Julia or Python or similar.For further reading, try Matrix Analysis and Applied Linear Algebra by Meyer.
 I was scrolling through to see if you explain how you typeset the math (notoriously hard on webpages), but I happened to instead find a small mistake. You write: "Elements of $\mathbb{R}^n$ are sets of real numbers." That is an incorrect definition.- It is inaccurate because n doesn't enter into the definition (and thus all Euclidean spaces would be the same).- You want ordered n-tuples, not sets. If you actually defined elements of R^n as sets of n real numbers, you would not be able to represent the diagonal (or, if you fix that, not be able to represent the difference between certain points on the diagonal of R^n and certain points on the diagonal of certain subspaces).Moreover, figure 5 talks about "overlapping vectors". This is highly non-standard, and definitely would need to be defined.Further, you're setting your readers up for trouble by defining vector arithmetic in terms of bases.
 Totally agree with this post...however, to be extremely pedantic (and thus not suitable for the article in question), a tuple in the foundations of mathematics is typically defined as a set. That is, (x,y) := {x,{x,y}}, where the latter is the set containing the element x and the set {x,y}. That is how one goes from axiomatic set theory to define tuples of numbers.
 There is a big difference between your type of pedantry versus the OP... I don't think the OP was pedantic. It is simply not a set of real numbers. He did say that it was a "small mistake".The first is more an error of understanding (for the lack of a better term), whereas talking about tuples as being de facto sets is truly about being pedantic.
 Absolutely! In this sense you are absolutely right, but a reader who knows how to construct such tuples (i.e. fill in the blanks in the article) also in all likelihood knows the content of the article. And I bet readers who don't know that already, will not realize that those are the sets the author means.After stumbling across the author's twitter where he already complains that people are "being mean on HN", and seeing his responses there, I have some serious doubts about whether he is fit to be teaching people mathematics. I honestly applaud him for writing the article, and don't hold the math mistake against him at all. But the incredible defensiveness when confronted with a small mistake is absurd.
 Who goes from axiomatic set theory at all, if their goal is not to be a logician/type theorist? One does not need to know axiomatic set theory to study linear algebra any more than one needs to know about semiconductors in order to program in Python.
 To be even more pointlessly pedantic: sure, but that doesn't give you "sets of real numbers", in the sense of sets where every element can meaningfully be interpreted as a real number.
 Oh and perhaps more immediately: with this definition of R^n, (x,y) and (y,x) are the same point. No good.
 Keep in mind those are just notes I made for myself. I decided to put them out there just in case someone found them useful and to signal my skill... By practicing ML/DS in the last couple of years, I came to realize that what I put there is probably more than what is needed to know for applied ML/DS, and conceptual inaccuracies like those have little to none relevance
 Well, wrong is wrong :-)I mean no offense by saying that, and it's human nature to be wrong.However, this is not a "conceptual inaccuracy". It's wrong. Straight up, old-fashioned wrong. And don't tell me it's of "little to no relevance" that your definition of R^2 does not distinguish between (0,1) and (1,0).
 Great resource. I also want to post this series by Rachel Thomas of Fast.AI.https://www.youtube.com/playlist?list=PLtmWHNX-gukIc92m1K0P6...She's a phenomenal teacher, and has grounding in the practice of applying it to ML and deep learning.
 Is there a website that anyone knows of for these types of open-source curriculums? Feel like it would be nice to have a place where people could post these and you could reference them when you wanted to learn something in the correct order and with the best resources.
 They’re much narrower in scope than a full curriculum (or even a course, for that matter), but Better Explained [0] has some very good overviews of math topics. They are a useful supplement I’ve come across repeatedly while searching topics I found challenging over the years.On the topic of open source learning, I take every chance I can to heartily recommend fast.ai’s course [1]. It’s a good intro to Deep Learning that leaves you informed enough to build things, and equips you to ask follow-on questions and dive deeper when/where you need to.
 Perhaps more relevant for this topic is the computational linear algebra course from fast.ai:https://www.fast.ai/2017/07/17/num-lin-alg/It has a lot more detail on stuff like floating point storage, memory layout, sparse matrices, iterative methods, etc than most linear algebra courses, but doesn't go much in to proofs, geometric interpretations, and other stuff that's less needed for algorithm design and implementation.(Disclaimer, I'm from fast.ai.)
 For AI/ML, I think https://madewithml.com/ does the job. It has curated open source projects, courses, papers and topics.
 Khan Academy is great, but I mean for all resources on a subject. In other words, a place where people can post curations of resources, not actual content. So say I wanted to learn linear algebra it would point to Khan Academy for the basics part and then other places as well.
 Something like this https://github.com/rossant/awesome-math ?
 The list of "awesome lists" on github [1] is generally quite helpful (haven't checked them all myself obviously).
 Thanks for this Pablo. I find this a good intro to LA as well as a tutorial on Numpy! Just one feedback would be good to have the TOC handy as we click around or a way to jump back to the top.
 This looks like an excellent resource. Thank you.The rendering of some of the Latex code does seem to be bit of a challenge; I see some intermingled code/text (on latest Mozilla on Ubuntu 18). The CPU usage also shoots up.What scripts are rendering the Latex code?
 It usually takes a while to render the LaTeX code in my browser. If you scroll down immediately after entering the site you may find it looking weird. I just used mathjax syntax which supposedly renders on most browsers (my blog is hosted on GitHub, using Jekyll as site-generator). My knowledge of web-development is very basic, so I might be doing some things wrong ( ˘︹˘ )
 Linear algebra: Everything is happy lad-dee-dah for x and y. The moment we go into matrices I go downhill from there. I saw a very cool youtube on Tesla Dojo and machine learning. I recommend.
 One of the fun things about linear algebra is that you’re working with lots of simple equations all at once. It’s like moving from single variable calculus to multi-variable calculus. You realize that the additional complexity was there all the time, and you were just studying a special, restricted case before.
 Yes, and it's super useful. The first times you find yourself working with several equations and you 'just' put that into a matrix form and solve that system is an amazing feeling of 'truth' having been hiding in plain sight.
 Absolutely. It’s easy to forget how useful it is to be able to solve a system of equations like that. It lets you find optimal settings for complex systems with multiple constraints. Fitting a machine learning model is just one application for this... there’s a whole academic discipline called Operations Research that focuses on using optimization to find solutions to practical problems.Just another example of the huge power in creating accurate digital models of the world.
 We touched a bit of that. As an aside, when I was a student, we also had an applications module called "Numerical Analysis". We went through a bunch of algorithms (Cholesky, Seidel, Newton-Raphson, Gauss, etc.) and ran them by hand. We basically were "human computers". The exams were also solving problems using these algorithms, and given the iterative nature of many of them, if you make a tiny mistake it'll ripple and ruin everything for you.As an aside, my background is in optimal control/control theory and instrumentation, and operational calculus, state space representations, and matrices were a huge part of the "Jiu-Jitsu" we did. Tinkering with RST control, robust systems, finding optimal systems and sequences (Hamilton-Jacobi-Bellman-Pontryagin) with matrices flying around on our exam papers solving these systems. It was a nice abstraction.Very, very, powerful tools that command immense respect for Laplace, Lagrange, and people like them who invented things to solve problems we're facing now.
 It's not on the syllabus, but what application does jordan canonical form have to machine learning?
 probably none, since afaik the Jordan normal form is numerically very unstable. It's however quite useful in proofs (e.g. you can theoretically construct the matrix exponential out of it).
 here's a Linear Algebra course from Columbia University with a bit of computer science emphasis. https://tonydear.github.io/teaching/coms3251
 are there resources where linear algebra is discussed in the context of deep learning?
 Accompanying the book in the sibling comment is Strang's MIT 18.065 course which is exactly what you're after (it specifically covers linear algebra with a focus on data science and ML): https://ocw.mit.edu/courses/mathematics/18-065-matrix-method...OCW so it's free(!), including the videos and handouts.
 And Strang (more than) knows what he's talking about. Unlike OP, who treats minor corrections as personal attacks and goes all defensive. This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.
 > This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book. The only thing that is important is the quality of the resource, not where it came from.Strang's free videos are great. That's the important thing to share.(I edited to clarify which part of the parent comment I took issue with).
 > Please don't gatekeep education like this. I've caught teachers from established institutions in mistakes hundreds of times in my life, and often just as defensive. And I've found "random blogs" on the internet that explain things far clearer than the school recommended book.Absolutely! And I've had medical doctors make lots of mistakes, while random blogs on the Internet have been right. Buuuut, you know.> The only thing that is important is the quality of the resource, not where it came from.Right. And the blog author we're discussing is flat out refusing to accept that his material has basic mistakes. That's a gigantic red flag. Again: it's not about being wrong. It's about refusing to accept that he's wrong.
 > Buuuut, you know.No I don't. Could you please explain? If random blogs have helped you catch doctors making mistakes (like they have me) then it would seem to strengthen my point that gatekeeping sources of valuable information based on their origin instead of their quality is a mistaken approach.
 What I mean is: even after experiencing that, I'm gonna see a medical doctor for medical problems. I bet you will too, if the problem is serious enough.
 We are discussing how and where we learn things. So the fact that I go to a mechanic to fix my car has little to do with gatekeeping about where I should learn about how to fix my car, or learn enough to keep my mechanic honest.
 Well, if the blogpost that taught you how to fix your car has an elementary mistake that the author refuses to acknowledge and gets super defensive about, it's sure time to take a step back. Does it mean all blogs are bad? Of course not. But if you have the option of listening to a world-renowned mechanic instead, for free, I'd say you should.
 > This is part of the reasons why it's dangerous to replace education from established institutions with random blogs on the internet.> If you have the option of listening to a world-renowned mechanic instead.With the note that "world-renowned" has almost nothing to do with "education from established institutions" I feel like we've made progress here, so I'll leave it at that.
 "Linear Algebra and Learning from Data" by Gilbert Strang [1] has a section on that.
 This is so wonderful. Thank you for putting this up :)
 This is sick! I'm saving this for sure.I also really appreciate linking to other learning materials in the beginning (both free and non-free)

Applications are open for YC Summer 2021

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text:
# Convergence articles

Displaying 101 - 110 of 649

This is the title page of the first textbook in the calculus of variations, Leonhard Euler's Method of Finding Curved Lines that Show some Property of Maximum or Minimum. It was published in 1744.
Now a good horse and an inferior horse set out from Chang'an to Qi. Qi is 3000 li from Chang'an.
A translation of one of the seminal papers in the field of elliptic integrals, but one that can be read by an undergraduate.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay? Problems from a 15th century French manuscript, including one with negative solutions Convergence Advisory Board 2004-2009 Here is the title page of part I of the General Trattato di Numeri (General Treatise on Number and Measure) (1556) of Niccolo Tartaglia (1500-1557). This is an extensive work on elementary mathematics that was popular in Italy for several decades after its publication. A farmer sold a team of horses for$440, but did not receive his pay for them until 1 yr, 8 mo after the sale. He had at the same time another offer of \$410 for them. Did he gain or lose by the sale and by how much, money being worth 6%/yr?
Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
A song for Pi Day.


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1. ## Homework help pls!

Hi, i need some help on my homework which is due tml. Here goes:

Let X1,...,Xn be i.i.d. U(0, $\theta$) random variables. Let Yn be the maximum of X1,...,Xn.

Yn = max {X1, ... ,Xn}.

a) Determine a sequence ${k_{n}}$ of constants, $k_{n} \uparrow + \infty$ as n $\uparrow + \infty$, such that $lim_{(n \rightarrow + \infty )} P(k_{n} (\theta - Y_{n} \leq x) = G(x)$; the limit of G is a continuous distribution function you have to determine.

b)

2. Originally Posted by Questions
Hi, i need some help on my homework which is due tml. Here goes:

Let X1,...,Xn be i.i.d. U(0, $\theta$) random variables. Let Yn be the maximum of X1,...,Xn.

Yn = max {X1, ... ,Xn}.

a) Determine a sequence ${k_{n}}$ of constants, $k_{n} \uparrow + \infty$ as n $\uparrow + \infty$, such that $lim_{(n \rightarrow + \infty )} P(k_{n} (\theta - Y_{n} \leq x) = G(x)$; the limit of G is a continuous distribution function you have to determine.

b)


text:
## This Week's Seminars and Colloquia

### The asymptotic dimension of big mapping class groups

Series
Geometry Topology Seminar
Time
Monday, January 25, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Yvon VerberneGeorgia Institute of Technology

Dan Margalit is inviting you to a scheduled Zoom meeting.

https://zoom.us/j/94410378648?pwd=TVV6UDd0SnU3SnAveHA1NWxYcmlTdz09

Meeting ID: 944 1037 8648

Passcode: gojackets

In 2010, Bestvina-Bromberg-Fujiwara proved that the mapping class group of a finite type surface has finite asymptotic dimension. In contrast, we will show the mapping class group of an infinite-type surface has infinite asymptotic dimension if it contains an essential shift. This work is joint with Curtis Grant and Kasra Rafi.

### Monte Carlo methods for the Hermitian eigenvaue problem

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 25, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
ONLINE https://bluejeans.com/884917410
Speaker
Robert WebberCourant Institute

In quantum mechanics and the analysis of Markov processes, Monte Carlo methods are needed to identify low-lying eigenfunctions of dynamical generators. The standard Monte Carlo approaches for identifying eigenfunctions, however, can be inaccurate or slow to converge. What limits the efficiency of the currently available spectral estimation methods and what is needed to build more efficient methods for the future? Through numerical analysis and computational examples, we begin to answer these questions. We present the first-ever convergence proof and error bounds for the variational approach to conformational dynamics (VAC), the dominant method for estimating eigenfunctions used in biochemistry. Additionally, we analyze and optimize variational Monte Carlo (VMC), which combines Monte Carlo with neural networks to accurately identify low-lying eigenstates of quantum systems.

### Prague dimension of random graphs

Series
Graph Theory Seminar
Time
Tuesday, January 26, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
He GuoGeorgia Institute of Technology

The Prague dimension of graphs was introduced by Nešetřil, Pultr and Rödl in the 1970s. Proving a conjecture of Füredi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order $n/\log n$ for constant edge-probabilities. The main new proof ingredient is a Pippenger–Spencer type edge-coloring result for random hypergraphs with large uniformities, i.e., edges of size $O(\log n)$. Based on joint work with Kalen Patton and Lutz Warnke.

### A Polynomial Roth Theorem for Corners in the Finite Field Setting

Series
Analysis Seminar
Time
Wednesday, January 27, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09
Speaker
Michael LaceyGeorgia Tech

An initial result of Bourgain and Chang has lead to a number of striking advances in the understanding of polynomial extensions of Roth's Theorem.
The most striking of these is the result of Peluse and Prendiville which show that sets in [1 ,..., N] with density greater than (\log N)^{-c} contain polynomial progressions of length k (where c=c(k)).  There is as of yet no corresponding result for corners, the two dimensional setting for Roth's Theorem, where one would seek progressions of the form(x,y), (x+t^2, y), (x,y+t^3) in  [1 ,..., N]^2, for example.

Recently, the corners version of the result of Bourgain and Chang has been established, showing an effective bound for a three term polynomial Roth theorem in the finite field setting.  We will survey this area. Joint work with Rui Han and Fan Yang.

The link for the seminar is the following

https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09

### Serre Spectral Sequence

Series
Geometry Topology Student Seminar
Time
Wednesday, January 27, 2021 - 14:00 for
Location
ONLINE
Speaker
Hugo Zhou

I will introduce Serre spectral sequences, then compute some examples. The talk will be in most part following Allen Hatcher's notes on spectral sequences.

### Representations of Sl(2,C) in combinatorics

Series
Student Algebraic Geometry Seminar
Time
Friday, January 29, 2021 - 09:00 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Trevor GunnGeorgia Tech

There are two purposes of this talk: 1. to give an example of representation theory in algebraic combinatorics and 2. to explain some of the early work on unimodal/symmetric sequences in combinatorics related to recent work on Hodge theory in combinatorics. We will investigate the structure of graded vector spaces $\bigoplus V_j$ with two "shifting" operators $V_j \to V_{j+1}$ and $V_j → V_{j-1}$. We will see that this leads to a very rich theory of unimodal and symmetric sequences with several interesting connections (e.g. the Edge-Reconstruction Conjecture and Hard Lefschetz). The majority of this talk should be accessible to anyone with a solid knowledge of linear algebra.

https://teams.microsoft.com/l/meetup-join/19%3a3a9d7f9d1fca4f5b991b4029b09c69a1%40thread.tacv2/1611606555671

### The differential equation method in Banach spaces and the n-queens problem

Series
Combinatorics Seminar
Time
Friday, January 29, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke
Speaker
Michael Simkin

The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
We apply this tool to the classical n-queens problem: Let Q(n) be the number of placements of n non-attacking chess queens on an n x n board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing n queens on the board. Furthermore, we can obtain a complete n-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that Q(n) \geq (n/C)^n, for a constant C>0 associated with the ODE. This is optimal up to the value of C.

Based on joint work with Zur Luria.


text:
# Package trackchanges : option “margins” buggy? [closed]

According to the documentation of trackchanges, the option "margins" should allow to write the comments in the margins :

\documentclass[12pt]{article}
\usepackage[margins]{trackchanges}
\begin{document}
Before-Text  \annote{text}{comment}
\end{document}

but it won't compile. With the option "inline" instead of "margins" it works. Did someone else encounters the problem ?

-
Works fine for me: 'too localized' –  Joseph Wright Mar 3 '12 at 21:48


text:
## Algebra 2 (1st Edition)

$x\gt\frac{c-b}{a}$ or $x\lt\frac{-c-b}{a}$.
$|ax+b|\gt c$ implies $ax+b\gt c\\ax\gt c-b\\x\gt\frac{c-b}{a}$ or $ax+b\lt -c\\ax\lt -c-b\\x\lt\frac{-c-b}{a}$. Thus $x\gt\frac{c-b}{a}$ or $x\lt\frac{-c-b}{a}$.


text:
# [particle physics] Decay of baryon

1. May 28, 2012

### nonequilibrium

1. The problem statement, all variables and given/known data
Are the following reactions possible? If yes, explain why and how the reaction occurs. If no, explain why.

...

$\Delta^+ \to p^+ + \pi^0$"

2. Relevant equations
NA

3. The attempt at a solution
First of all, it wouldn't break any conservation law, hence it is possible (or is this reasoning faulty? In other words is there an example of something not breaking any conservation law, even kinematically, yet not happening since it has no possible Feynman diagram?)

Now, although I'm sure it's possible, I'm not sure what to answer on "how the reaction occurs": am I right in thinking that it is possible through all three interactions? (strong, electromagnetic, weak)

I can think of two sensible things to answer: either list all possible reactions, or list the dominant one (always the strong force when possible via that interaction?). Which of the two is most sensible? And to specifically describe that strong interaction, I would draw the following beautiful picture

Is this correct? And is it also of lowest order, or am I overlooking something simpler? (am I right in thinking that I can NOT leave out the second gluon, cause otherwise that branch on the right hand side would be detached from the other branch, which is not allowed (?))

EDIT: on second thought, the first gluon seems superfluous?

#### Attached Files:

• ###### decay.gif
File size:
7 KB
Views:
139
2. May 29, 2012

### fzero

Yes, it is. The single gluon diagram is dominant.


text: Hi, I am trying to generate 12*2 matrix. That is a different matter than constructing matrices whose entries have a uniform distribution within a given range and the matrix as a whole is PD. This MATLAB function returns an n-by-n distributed matrix with random integer values in the range [1,imax]. R = normrnd(mu,sigma) generates random numbers from the normal distribution with mean parameter mu and standard deviation parameter sigma. This example shows how to create an array of random integer values that are drawn from a discrete uniform distribution on the set of numbers –10, –9,...,9, 10. Indexing into a matrix is a means of selecting a subset of elements from the matrix. Question: (a) Using MATLAB's Randi Function, Create A 12 X 12 Matrix Of Random Integers, Each In The Inclusive Range From - 10 To 10, And Assign The Matrix To Variable A. I'm trying to generate a random integer in the range of -5 and +5 using round and rand functions. Use rand, randi, randn, and randperm to create arrays of random numbers.. Random Numbers Within a Specific Range. The first column should contain random values between [0 5] and the second column should have random values between [5 20]. Thanks for your feedback Cedric. Random Matrix with Integer values; Random Matrix with a specific range of numbers; Matrix with desired size ( User can choose the number of rows and columns of the matrix ) Create Matrix of Random Numbers in Python. To get normally distributed random numbers with mean and standard deviation other than the standard normal distribution ($\mu=0,\sigma=1$), you will have to use another MATLAB builtin function normrnd(),. Learn more about matrix, function So you can either type "help random" "doc random" into the command window, or click the question mark icon, or (in older versions) get help from the menus. y = range(X,vecdim) returns the range over the dimensions specified in the vector vecdim.For example, if X is a matrix, then range(X,[1 2]) is the range of all elements in X because every element of a matrix is contained in the array slice defined by dimensions 1 and 2. Learn more about positive semidefinite matrix, random number generator Random Numbers Within a Specific Range. There is a help facility in MATLAB (beyond the Answers forum). The plot is formed by joining adjacent points with straight lines. Generating a random matrix with range. I only want to pick one element which is what the above does. The rank gives a measure of the dimension of the range or column space of the matrix, which is the collection of all linear combinations of the columns. 0. selecting a specific range in a matrix and cell array. Also had problem with perms (needed to restart Matlab to be able to generate for 11 elements, I have x64 and 16GB of memory). y = range(X,vecdim) returns the range over the dimensions specified in the vector vecdim.For example, if X is a matrix, then range(X,[1 2]) is the range of all elements in X because every element of a matrix is contained in the array slice defined by dimensions 1 and 2. 0 ⋮ Vote. matrix random number generator. Learn more about matrix normalization (b) Create A Row Vector B Storing In Each Of Its Elements The Number Of Zeros Occurring In The Corresponding Column Of Matrix A. I'm able to generate a random integer however it always returns a negative value and a zero and not in the expected range. In matlab, one can generate a random number chosen uniformly between 0 and 1 by x = rand(1) To obtain a vector of n random numbers, type x = rand(1,n) If you type x = rand(n) you get a n-by-n matrix of random numbers, which could be way too big. It's right there built into MATLAB. It is used in many programming languages for the generation of random values within the specified range. MATLAB ® graphics defines a surface by the z-coordinates of points above a rectangular grid in the x-y plane. We will create each and every kind of random matrix using NumPy library one by one with example. This MATLAB function returns an n-by-n distributed matrix with random integer values in the range [1,imax]. Create Arrays of Random Numbers. Random Integers. for example i want to select all the elements that are lower than 182 and swap/change them. Learn more about matrix, random number generator In cases where both are important a better solution would be to expand the bounds by a very very small amount near the limit of Matlab's precision and then to include a conditional that checks if a value was drawn outside of the bounds. There usually is values above and below .5. I'm looking for a way to generate a *random positive semi-definite matrix* of size n with real number in the *range* from 0 to 4 for example. Unlike rand and randn, a parameter specifying the range must be entered before the dimensions of the matrix. Best Answer. Nearly all random matrices are full rank, so the loop I show will almost always only iterate once and is very very unlikely … positive semidefinite matrix random number generator. This example shows how to create an array of random floating-point numbers that are drawn from a … selecting a specific range in a matrix and cell array. Learn more about random number generator, random, homework MATLAB Vote. This example shows how to create an array of random floating-point numbers that are drawn from a uniform distribution in the open interval (50, 100). Random Number Generator is the creation of random numbers without any decision or noticeable patterns among them. Answered: Image Analyst on 23 Dec 2014 ... And since MATLAB passes implicitly by reference anyway, it won't require a memory copy unless you … Learn more about matrix, random number generator Can you help me out with this. 0. Follow 90 views (last 30 days) AA on 23 Dec 2014. Let’s get started. For example, let us create a 4-by-5 matrix a − For things like this you can use the help documentation. Save the current state of the random number generator and create a 1-by-5 vector of random numbers. Vote. How to generate a random matrix ?. Surface plots are useful for visualizing matrices that are too large to display in numerical form and for graphing functions of two variables. Than I decided to keep characters instead of the numbers, reducing the memory occupied by the matrix. Generate Random Numbers. Representing Data as a Surface Functions for Plotting Data Grids. So all we have to do is generate an initial random matrix with full rank and we can then easily find a positive semi-definite matrix derived from it. s = rng; r = randn(1,5) r = 1×5 0.5377 1.8339 -2.2588 0.8622 0.3188 How can normalize matrix in range [-1,1]?. I'd bet that the need for a random process would have higher importance than the need for the very small chance of hitting the bounds. Answered: Image Analyst on 23 Dec 2014 ... And since MATLAB passes implicitly by reference anyway, it won't require a memory copy unless you … The simplest randi syntax returns double-precision integer values between 1 and a specified value, imax. Generating a random matrix with range. 0 ⋮ Vote. Indexing is a key to the effectiveness of MATLAB at capturing matrix-oriented ideas in … I wil apply it in the future to a matrix of zeros and 1's and apply a random movement to the element picked. A matrix is full rank if its rank is the highest possible for a matrix of the same size, and rank deficient if it does not have full rank. Generate a 2x3 matrix of random: real numbers, each in range 0 to 1; real numbers, each in range 0 to 10; integers, each in range 5 to 20. In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row. MATLAB ® has several indexing styles that are not only powerful and flexible, but also readable and expressive. MATLAB: How to generate a random positive semi-definite matrix of certain size with real numbers in a certain range. There are various ways of generating random numbers in MATLAB with different applications. does someone know an easy way or command to do this in matlab ? Such matrices appear to be relatively rare to start with; to require uniform random distribution on the entries appears to make them difficult to generate. I know how to make matrices with random numbers and make all the random numbers necessary, I'm just confused. In the following example, a 2 x 4 matrix of random integers in the range of [1, 10] is created. The following command creates a matrix of random integers of size m x n in a range from 1 to x. Be careful not to confuse rand with randn, which produces Gaussian random variables. This MATLAB function returns an n-by-n distributed matrix with random integer values in the range [1,imax]. I have a matrix and i want to select a range of elements. MATLAB: Generating a random matrix with range. A matrix is a two-dimensional array of numbers. 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Enter the total monthly savings and monthly gross income into the calculator to determine your savings rate.

## Savings Rate Formula

The following formula is used to calculate a savings rate:

SR = MS/MI *100
• Where SR is the savings rate (%)
• MS is the montly savings ($) • MI is the monthly gross income ($)

## Savings Rate Definition

A savings rate is defined as the ratio or percentage of monthly gross income that an income or household is able to save each month after all expenses are paid for.

For example, if an individual earns $5,000 per month and they are able to save$2500 per month, then the savings rate is 50% because they are saving half of their income.

## What is a good savings rate?

In general, a savings rate of anything above 15% is considered extremely good. The higher a person’s income, the higher their savings rate should be.

## Example Problem

How to calculate a savings rate?

1. First, determine the total monthly gross income.

For this example, we are looking at a household with monthly incomes of $4000 and$6000 from the heads of the household respectively. This leads to a total income of $10,000.00. 2. Next, determine the total monthly savings amount. In this case, the household is only able to save$1000.00.

3. Finally, calculate the savings rate.

Using the formula above, the savings rate is calculated as:
SR = MS/MI *100
SR = 1000/10000 *100
SR = 10%.