Products of orthogonal projections and polar decompositions

Details Products of orthogonal projections and polar decompositions Products of orthogonal projections and polar decompositions

2010-11-23

arxiv.org/abs/1011.5237v1

Mathematics

Functional Analysis

Scientific paper

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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