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Let $A_i$, $B_i$ be hermitian $n$ by $n$ positive semidefinite matrices of rank $1$, for $i = 1, \dots, n$. Assume that the rank of $A_i \circ B_i$ is also $1$, for $i = 1, \dots, n$, where $\circ$ ...

Motivation: I am faced with a $5 \times 5$ hermitian positive semidefinite matrix, depending on parameters, and I wish to show that it is positive definite, for any points in the parameter space (I ...

$\DeclareMathOperator{\tr}{tr}$ Fix an integer $n \geq 2$. Let $A_1, \dotsc, A_n$ be hermitian positive semidefinite matrices, with each $A_i$ being $m$ by $m$. Consider the symmetric group $S_n$ on $...

While working on the Atiyah problem on configurations of points, I came across formulas involving products of traces of products of singular hermitian positive semidefinite $2$ by $2$ matrices. To ...

In my question I am considering $z$ as the complex variable in the $z$-transform $X(z)$ of a discrete-time sequence $x[n]$: I have $M$ square complex matrices $\mathbf{R}_m$ of size $N\times N$. I ...