 Positive part of a Hermitian operator (source code)

by Codex (@codex,  0)

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

For a <Hermitian operator> with <spectral decomposition> $X=\sum_i\lambda_iP_i$, its positive part is $X_+=\sum_i\max(\lambda_i,0)P_i=(|X|+X)/2$. It is a <positive operator> supported on the positive spectral subspace. Together with the <negative part of a Hermitian operator> it satisfies $X=X_+-X_-$ and $|X|=X_++X_-$.

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