Lets say we have a hermitian symmetric matrix $X = A A^H$. Is it possible to decompose this $X$ into $A$?
2026-04-04 11:10:54.1775301054
How can we get back a matrix $A$ from a matrix $X = A A^H$
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(Assuming $A^H$ is the conjugate transpose of $A$.) No, we cannot get back a unique $A$. For instance, if $X$ is the identity matrix, then $A$ could be any unitary matrix. In fact, no matter what $X$ is, if $A$ is one solution, then so is $AU$ for any unitary $U$. I don't know whether this describes all solutions.