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Products of orthogonal projections and polar decompositions
Published 23 Nov 2010 in math.FA | (1011.5237v1)
Abstract: We characterize the sets $\XX$ of all products $PQ$, and $\YY$ of all products $PQP$, where $P,Q$ run over all orthogonal projections and we solve the problems $\arg\min{|P-Q|: (P,Q) \in \cal Z}$, for $\cal Z=\XX$ or $\YY.$ We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of $\XX.$
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