Approximation by partial isometries and symmetric approximation of finite frames

ANTEZANA, JORGE; CHIUMIENTO EDUARDO

Ames

Congreso; 2017 Meeting of the International Linear Algebra Society (Iowa State University); 2017

Iowa State University

We solve the problem of best approximation by partial isometries of givenrank to an arbitrary rectangular matrix, when the distance is measured in any unitarilyinvariant norm. In the case where the norm is strictly convex, we parametrize allthe solutions. In particular, this allows us to give a simple necessary and sufficientcondition for uniqueness. We then apply these results to solve the global problem ofapproximation by partial isometries, and to extend the notion of symmetric approximationof frames