# Tagged Questions

30 views

### Generate random symmetric positive-definite matrix

Is there a simple way to generate a random matrix that is symmetric and positive-definite? The symmetry seems like it could be achieved by generating a matrix $M$ with independent random entries and ...
57 views

### Generate some random matrix with given rank

Very often for creating new exercises (I teach basic matrix algebra), I need to a find a matrix $A$ such that: it has integer coefficients, not too big (in order to avoid big numbers computations) ...
42 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 ...
32 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. ...
129 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 ...
266 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: ...
646 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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### 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 ...
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 ...