Absolute value of an operator
= Absolute value of an operator
{title2=$|L|=(L^\dagger L)^{1/2}$}
= Operator absolute value
{synonym}
The absolute value of a <linear operator> $L$ is the <positive square root of an operator> $L^\dagger L$. Its <eigenvalues> are the <singular values> of $L$, its <trace> is the <trace norm> of $L$, and it appears in the <polar decomposition of a bounded operator> $L=U|L|$.