REVERSE ORDER LAWS FOR GENERALIZED INVERSES OF MULTIPLE MATRIX PRODUCTS

By using the ranks of matrices, this article gives necessary and sufficient conditions for the reverse product A(n)+ ... A2+A1+ of the Moore-Penrose inverses of A1, A2,...,A(n) to be a {1}-inverse (inner inverse), {1, 2}-inverse (reflexive inner inverse), {1,3}-inverse, {1,4}-inverse, inverse, {1,2,3}-inverse, {1,2,4}-inverse, or Moore-Penrose inverse of matrix product A = A1A2...A(n).