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For Given a $N×M$ random complex gaussian matrix $X$ where $M=XX^H$, let $\lambda_1>\lambda_2>\cdots>\lambda_N$ be the ordered eigenvalues of $M$ my objective is to get an estimation of $$ f = \left(\ …

Given a $N×M$ random complex gaussian matrix $X$ and $N×K$ random complex gaussian matrix $Y$ I'm interested in approximating the expectation expressed as: \begin{align} E[trace({(aX{X^H} + I)^{ - …

Let $\lambda_1>\lambda_2>....>\lambda_N$ be the ordered eigenvalues of Wishart matrix my objective is to find if it is possible the distribution of: \begin{align} s = \sum\limits_{i = 1}^N {\frac{ …

Let $X$ be an $(N, M)$ random Gaussian matrix where $M<N$. For a given vector $v$, I want to estimate the expectation of: \begin{align} E\left[ {{v^T}X{X^T}{v}} \right] \end{align} and \begin{align} E …

Let $A$ be $(n,n)$ central Wishart matrix with $k$ degrees of freedom. my question is there is a way to estimate the expectation of: \begin{align} E[det(I+(I+A)^{-1})] \end{align}

Let $X(N,N)$ be Wishart matrix with rank(X)=K in order to estimate the expectation of the trace of the square root of X i.e $X^{1/2}$ I want to know if is possible to use the unordered Wishart distri …

the singular value decomposition of an $m\times n$ random Gaussian matrix ${\displaystyle \mathbf {M} }$ is a factorization of the form ${\displaystyle \mathbf {U\Sigma V^\ast} }$, ${\displaystyle \ …

This question is related to another answered before distribution on the inverse Wishart matrix eigenvalues summation my question is, is their finite expression for the expectation of \begin{align} {\r …

I am trying to obtain an Approximating expectation of exponential of Wishart matrix $X (N,N)$ with $\operatorname{rank} (X)=K$defined as: \begin{align} J = E[{e^{{v^H}Xv}}] \end{align} where $v$ is …

In order to characterize the performances of MIMO systems that depend directly on the distribution of the eigenvalues of random Hermitian matrix so I would like to feature the quality of some particul …