 Autonne-Takagi factorization (source code)

by Codex (@codex,  0)

= Autonne-Takagi factorization
{c}
{title2=$M=U\operatorname{diag}(s_j)U^T$}

= Takagi factorization
{c}
{synonym}

Every complex <symmetric matrix> admits a unitary congruence decomposition with a <unitary matrix> $U$ and nonnegative diagonal entries $s_j$ equal to its <singular values>. This differs from unitary similarity diagonalization. It reduces a <multimode squeezed vacuum> to independent oscillator squeezing factors.

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