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1answer
37 views

Algorithm to generate normal matrices at random

I would like to generate normal matrices by an, say python, algorithm, that produces normal matrices distributed evenly in the limit of large n. I would not like to be restricted to Hermitian matrices ...
1
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1answer
29 views

linear dependncy of a random vector with respect to a reduced row echelon form in a finite field

Given a matrix with elements from a finite field $\mathbb{F}_q$, $A\in\mathbb{F}_q^{N\times M}$, where $q$ is the size of the field, $N<M$. Suppose that $A$ in the reduced row echelon form. ...
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0answers
111 views

Variance of the first return time of a simple random walk on an hypercube graph

I am trying to solve this problem.... I have a simple random walk on a $d$-cube (finite graph). At each vertex of the graph, the particle chooses one of $d$ edges equally likely. I need to calculate ...
1
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1answer
232 views

Normal distributed rotation matrix in 3D

How can I compute normally distributed 3D rotation matrices with Mathematica? For 2D matrices I would sample a normal distributed angle and directly create a rotation matrix with: ...
3
votes
3answers
485 views

How to randomly construct a square full-ranked matrix with low determinant?

How to randomly construct a square (1000*1000) full-ranked matrix with low determinant? I have tried the following method, but it failed. In MATLAB, I just use: n=100; A=randi([0 1], n, n); while ...
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1answer
35 views

what should be the frequency distribution of the eigenvalues of a randomly generated hermitian matrix?

I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a ...
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1answer
63 views

How to prove that the expression E(z'Az) (for a random vector z) is …

I am looking to prove the following Let $z$ be an $m\times$ 1 random vector with $E(z)=\mu$ and $\operatorname{Cov}(z)=V$ and let $A$ be an $m\times m$ non-stochastic matrix. Then the following ...
7
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2answers
256 views

Accessible Intro to Random Matrix Theory (RMT)

I read this fascinating article: http://www.newscientist.com/article/mg20627550.200-enter-the-matrix-the-deep-law-that-shapes-our-reality.html Unfortunately all the other papers I find googling are ...