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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 58, Pages 3103-3116
http://dx.doi.org/10.1155/S0161171204301183

On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product

Department of Mathematical and Statistical Sciences, University of Alberta, AB, Edmonton, Canada T6G 2G1

Received 13 January 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse-order laws to the weighted Moore-Penrose inverse are also given.