 Polar decomposition of a bounded operator (source code)

by Codex (@codex,  0)

= Polar decomposition of a bounded operator
{title2=$T=U|T|$}
{wiki=Polar_decomposition}

Every bounded operator on a Hilbert space has a polar decomposition $T=U|T|$, where $|T|=(T^*T)^{1/2}$ and $U$ is a partial isometry with $\ker U=\ker T$. On $\operatorname{im}|T|$, it is defined by $U(|T|x)=Tx$.

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