# Questions tagged [random-matrix]

A random matrix is a matrix whose entries consist of random variables from some specified distribution. Random matrices have many modern applications in physics, finance, statistics and numerical analysis.

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### Does $E(XX^{\top})$ being full rank imply $E(XX^{\top}\mathbf{1}(Y\in A))$ being full rank?

suppose $X=\begin{bmatrix}X_{1}\\X_{2}\end{bmatrix}$ is a discrete random vector with finite support, and $Y$ is a continuous random variable with finite support $[a,b]$, and $A$ is a subset of $[a,b]$...
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### (Co)Variance of a random matrix

The expected value $\mathbb{E}[\mathbf{x}]$ of a random vector $\mathbf{x} \in \mathbb{R}^{n \times 1}$ is the vector of the expected values of each individual random variable $\mathbf{x}$ contains. ...
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### Why linear transformation can improve classification accuracy when the dimensionality of data is high?

Let $X$ be an $m\times n$ ($m$: number of records, and $n$: number of attributes) dataset. When the number of attributes $n$ is large and the dataset $X$ is noisy, classification gets more ...
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### Generating random variables satisfying constraints

I need to generate a list of random variables $\bf{x}$ subject to constraints that can be expressed in the form $\bf{E}x=b$ where $\bf{E}$ is an $m \times n$ matrix if $\bf{x}$ has $n$ entries. In ...
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### Generating random matrices with sum and maximality constraints

I'd like to generate a random square matrix such that the rows are normalized to one and the diagonal elements are the maximum of their column. If there an efficient way to sample these matrices ...
Suppose I want to generate a $n \times n$ orthogonal matrix $H$ (that is, $H^T H=I$) but with the property that $1-e < (tr H)/n < 1+e$ for some pre-specified tolerance $e$. How can I do this? ...
Suppose I want to generate a nonnegative $n \times n$ matrix $\mathbf A$ for an odd $n$ (say, $n=5$ for a good enough example), such that the individual elements are drawn from a uniform distribution ...