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Seeking insights on bounded set positive solutions for a set of linear systems in $\mathbb{R}^n$
Before delving into my query, I'd like to provide some context. Consider a continuous function $f:\mathbb{R}^{k}\rightarrow\mathbb{R}^{m}$ and a compact set $\mathcal{B}\subset \mathbb{R}^{k}$ (...
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Finding a specific solution to $X^T\Sigma X = D$
I'm looking to solve for a specific $X$ in the following equation:
$$X^T\Sigma X = D,$$
where $\Sigma \succ 0$, $D$ is a diagonal matrix with strictly positive entries, and all matrices are square. It ...
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