International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 58, Pages 3103-3116
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 T6G 2G1, Canada
Received 13 January 2003
Copyright © 2004 Yongge Tian. 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.
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.