Let $A\in \mathbb{C}^{ n\times n}$ be a Hermitian matrix then find a matrix $X$ such that $X^*AX=B$ where $B \in \mathbb{C}^{p \times p}$ is a given Hermitian matrix and $p< n$.
Find a matrix $X\in \mathbb{C}^{ n\times p}$
Saheb
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