# Tagged Questions

The tag has no usage guidance.

7 views

### Hypothesis testing for matrices of RVs

I looking for the correct statistical test for comparing matrices of random variables - my IV being a categorical variable and my DVs being n by n matrices of random variables (which are themselves ...
51 views

### Write $\mathop {\mathbb E}[(X AX^h)]$ in function of $\mathop {\mathbb E}[(X X^h)]$?

Suppose $X$ is an $i \times j$ random matrix. In addition, $X$ has complex i.i.d. normal entries with $0$ as mean. We define $A$ (of dimension $j \times j$) as a deterministic matrix. Is it ...
41 views

### How to check if a distribution has undefined variance?

How can I determine if experimental data comes from a distribution where the variance is undefined (e.g. the Cauchy distribution)? I honestly have no idea how to attack this problem in a sensible way,...
8 views

### How to determine if a lower rank approximation exists?

In all the literature I read on low-rank approximations, I have yet to run across situations in which people first check to see if a lower rank exists. My understanding is that a matrix whose ...
20 views

69 views

### 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 ...
33 views

1k views

### 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 ...
780 views

### 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 ...
118 views

### Generation of orthogonal matrices “close” to identity

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? ...
319 views

### Generating random matrices with specific equality constraints

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 ...
867 views

### Random matrices with constraints on row and column length

I need to generate random non-square matrices with $R$ rows and $C$ columns, elements randomly distributed with mean = 0, and constrained such that the length (L2 norm) of each row is $1$ and the ...
Suppose I have an $N\times N$ covariance matrix that describes a multivariate normal joint distribution. Now take 100,000 draws of the covariance matrix. I measure the variance of values for each ...