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Answer by Will Jagy for Eigenvectors of a symmetric matrix and orthogonality

$$ U' U = I$$$$ U (U'U) = UI = U $$associativity$$ (UU') U = U $$cancel by multiplying on the right by the right inverse of $U$$$ UU' = I $$

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Eigenvectors of a symmetric matrix and orthogonality

Given a full rank symmetric matrix $A_{p\times p}$ we can build a matrix $U=[u_1,...,u_p]$ where $u_i$ is the eigenvector associated to the $i^{th}$ largest eigenvalue of $A$.Assuming that eigenvectors...

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