Abstract:
A proof of the following result, due to T. Crimmins, is proposed: A matrix $A\in M_n(\mathbf C)$ can be represented as a product of orthoprojectors $P$ and $Q$ if and only if $A$ satisfies the equation $A^2=AA^*A$.
Key words and phrases:orthoprojector, invariant subspace, unitary quasidiagonalizable matrices.
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