Let $A,B\in R^{n\times n}$ be symmetric matrices.
Given a matrix congruence relation:
$$ B = P^TAP $$
Is there an analytical solution or numerical algorithm for finding the transition matrix P?
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Find the eigenvectors for $A$ and $B$. Write them as $D_1 = P_1^T A P_1$. – GNUSupporter 8964民主女神 地下教會 Feb 10 '17 at 09:21
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can you please elaborate your answer? – user415012 Feb 10 '17 at 13:40
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This https://mathoverflow.net/questions/78106/solving-a-quadratic-matrix-equation might be of interest – yarchik May 02 '19 at 18:42