# Tagged Questions

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### What it means by “asymptotic normality” properties of a random matrix?

I know that for the case of a random variable and a random vector, one can using (multivariate) density of normal distribution and concepts of convergence to define an asymptotic normality of a random ...
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### The probability of getting a certain image by random pixelation

Well, seeing that I'm terribly bad at math I don't know how to solve this, I'll try to explain, excuse me if I sound dumb. Just suppose that I've got a photo/image with 320x240 resolution and 24 bit ...
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### 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 ...
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### random nonsingular matrices using matlab

Does anybody know how to generate a random nonsingular matrices using matlab? I use sprand (m, n , dens, 1)function to specify the condition number to be 1 right now.But it is too slow.Is there any ...
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### Random matrices in coordinate independent way

How to generate a random matrix in a basis independent way (so that the random distribution does not change if the coordinates are rotated)? I am especially interested in generating random rotation ...
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### 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) ...
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### Generating Different types of Matrices in Matlab

I am working on a project for a numerical methods class comparing two iterative methods for solving $Ax=b$, and I was wondering what type of functions Matlab has for generating arbitrarily large ...
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### Singular value of random matrix after linear transformation

Let $A$ a $n \times n$ random matrix with i.i.d $N(0,\sigma^2/n)$ entries. Let $H$ an invertible matrix, and denote $\sigma_H$ the largest singular value of $HAH^{-1}$. My question is : in the large ...
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### 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 ...
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### Entries of a Haar distributed unitary matrix

The eigenvector matrix of a Wishart matrix is Haar distributed and that implies that the eigenvectors are uniformly distributed on a sphere. I'm interested to know what is the distribution of ...
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### How to generate a N*D random matrix with columns of unit length?

Is it possible to generate a N*D random matrix with columns of unit length? If not, I also think it is possible of generating a N*D random matrix and, after that, normalizing it in order to have ...
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### What is the meaning of 'columns have unit lengths'

What is the meaning of this? In random projection, the original d-dimensional data is projected to a k-dimensional (k << d) subspace through the origin, using a random k × d matrix R ...
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### Generation of unimodular matrices with bounded elements

Does anybody know what is the algorithm for generating random unimodular matrices (integer matrices with determinant $\pm 1$) whose elements do not exceed a given bound? Such an algorithm is mentioned ...
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### how to Evaluate integral of density of Wishart matrix

Let $X_1 \cdots X_N$ are $N$ number of $m$ Dimensional Independent Complex Gaussian Random vectors Such that: $$X_j \sim \mathcal{N}(\mu,\Sigma)\; \forall \;j=1 \cdots N$$ Let ...
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### Modeling Sample Covariance Matrix based on concepts from Random Matrix Theory

I am working on a signal processing problem where I want to model the measurement sample covariance matrix (SCM) as random matrix and hence use the results from Random Matrix Theory (RMT). Let ...
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### Generating a random Eisenstein integer matrix whose inverse has Eisenstein integer entries

Thanks to a question I previously asked, I realized that a Gaussian integer matrix should have a determinant of $\pm 1$ or $\pm i$ for it to have an Gaussian integer inverse. From that, I gather that ...
### Invertible $N \times N$ matrix over ${\rm GF}(2)$ having on each row and column $N/2$ ones
As per the title, I'm looking for the name and for a way to construct a ${\rm GF}(2)$ square matrix of size $N$ with the following properties: All rows/columns should be linearly independent On each ...
Let $M$ be an $n \times n$ matrix whose elements are random reals in [0,1]. Two questions. What is the growth rate of the magnitude of the elements of $M^k$ as a function of $k$? It is definitely ...