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I am studying symmetric solutions to the complex matrix equation \begin{equation} A X B=C, \end{equation} where $A$, $B$, and $C$ are $m\times n$, $n \times k$, and $m \times k$ complex matrices, ...

I have a two matrices $A$ and $B$ in $\mathbb{R}^{m \times n }$ ($m \gg $ n) such that there exists an orthonormal matrix $X \in \mathbb{R}^{n \times n }$, such that: $$AX = B$$ Given that $X$ is ...

I need to solve the following equation for the matrix $P \in\mathbb{R}^{r\times d}:$ $$ ((PAP^\top)^{-1} P S P^\top (PAP^\top)^{-1})^2 = I_r, $$ where $S$ is a symmetric $d\times d$ matrix, $A$ is a ...