Products of orthogonal projections and polar decompositions

By Gustavo Corach, Alejandra Maestripieri. 2010

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e59d7a48d47e04cbf3258ecd20e462c81fa9b4ba