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I have a seemingly innocent linear algebra problem that I cannot solve, and which I hope that you would kindly offer some insight into. Here is the description: Let $\mathbf{a} = (a_1, a_2, \dots, a_d)...

Consider a fixed $N\times N$ positive definite symmetric matrix $A$. Assume $N=d^r$ for some $d,r\geq 1$. I wonder if one can find a closed formula for the maximizer/maximum of the function $$f(x):=\...

I have the matrix Product $PAP^H$ and I need to minimize $\|(PAP^H)^{-1}\|^2$ (over $P$ and Frobenius norm). $A$ is a positive definite Hermitian matrix and $P$ has the structure $$P=\left[\begin{...