Support of a positive operator
= Support of a positive operator
{title2=$\operatorname{supp}A=(\ker A)^\perp$}
The support of a <positive operator> is the <orthogonal complement> of its <kernel>. In finite dimension it is the span of <eigenvectors> with positive <eigenvalues>, equivalently the operator's image. <Quantum relative entropy> is finite only when the first state's support lies in the reference state's support.