By applying the product singular value decomposition of a matrix pair, some necessary and sufficient conditions for the existence of the are established and the limit expressions for some important generalized inverses are introduced.
15 March 2008 in Journal of Computational and Applied Mathematics
Necessary and sufficient conditions are obtained for a pair of matrix equations AX = C and XB = D to have common Re-nnd and Re-pd solutions and the explicit representations of the general common Re-nnd and Re-pd solutions are given when the stated conditions hold.