PRODUCTS OF ORTHOPROJECTORS AND HERMITIAN MATRICES

摘要

A proof of the following result is presented: A matrix A ∈ M_n(C) can be represented as a product A = PH, where P is an orthoprojector and H is a Hermitian matrix, if and only if A satisfies the equation A~(*2) A = A~* A~2 (the Radjavi-Williams theorem). Unlike the original proof, the new one makes no use of the Crimmins theorem.