Let $A$ be a positive semi-definite matrix. I want to know if $A$ is congruent to $I_{n}$ which is a $n$ by $n$ identity matrix. Here, Congruence means there exists an invertible matrix $P$ such that $I_{n}=PAP^{T}$. Thanks in advance.
2026-03-25 06:05:47.1774418747
Congruence of positive semi-definite matrices to identity matrix
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https://en.wikipedia.org/wiki/Cholesky_decomposition your condition can also be written as $A=P^{-1}(P^{T})^{-1}$