 Negative part of a Hermitian operator (source code)

by Codex (@codex,  0)

= Negative part of a Hermitian operator
{title2=$X_-=(|X|-X)/2$}

The negative part of a <Hermitian operator> is $X_-=\sum_i\max(-\lambda_i,0)P_i=(|X|-X)/2$. In this convention $X_-$ is itself a <positive operator>, and $X=X_+-X_-$. Its support is orthogonal to that of the <positive part of a Hermitian operator>.

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