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Rank equalities related to outer inverses of matrices and applications
Authors:Yongge Tian
Affiliation:1. Department of Mathematics and Statistics , Queen's University , Kingston, Ontario, K7L 3N6, Canada ytian@mast.queensu.ca
Abstract:A matrix X is called an outer inverse for a matrix A if XAX=X. In this paper, we present some basic rank equalities for difference and sum of outer inverses of a matrix, and apply them to characterize various equalities related to outer inverses, Moore-Penrose inverses, group inverses, Drazin inverses and weighted Moore-Penrose inverses of matrices.
Keywords:Rank  Outer inverse  Moore-Penrose inverse  Drazin inverse  Weighted Moore-Penrose inverse  AMS Subject Classifications:15A03, 15A09
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