Products of orthogonal projections and polar decompositions

Abstract

We characterize the sets X of all products P Q, and Y of all products P QP, where P, Q run over all orthogonal projections and we solve the problems arg min{kP − Qk : (P, Q) ∈ Z}, for Z = X or Y. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of X.