Now I am having some problems about the Wishart matrix. Please help me, thank you!
We know that $m \times m$ random matrix $\boldsymbol{A} = \boldsymbol{H} \boldsymbol{H}^H$ is a (central) real/complex Wishart matrix with $n$ degrees of freedom and covariance matrix $\boldsymbol{\Sigma}$ ($\boldsymbol{A} \sim \mathcal{W}_m (n, \boldsymbol{\Sigma})$), if the columns of the $m \times n$ matrix $\boldsymbol{H}$ are zero mean independent real/complex Gaussian vectors with covariance matrix $\boldsymbol{\Sigma}$.
My question is that: If the columns of matrix $\boldsymbol{H}$ are zero mean independent real/complex Gaussian vectors with different covariance matrix, i.e, the $i$-th column of $\boldsymbol{H}$ has covariance matrix $\boldsymbol{\Sigma}_i$ ($i=1, \cdots, n$). So what happen with matrix $\boldsymbol{A}$, is it Wishart matrix? and what is the distribution of $\boldsymbol{A}$?
Thank you again!
