WEIGHTED MOORE-PENROSE INVERSE OF A BOOLEAN MATRIX

If A is a boolean matrix, then the weighted Moore-Penrose inverse of A (with respect to the given matrices M, N) is a matrix G which satisfi es AGA = A, GAG = G, and that MAG and GAN are symmetric. Under certain conditions on M, N it is shown that the weighted Moore-Penrose invers e exists if and only if ANA(T)MA = A, in which case the inverse is N(T )A(T)M(T). When M, N are identity matrices, this reduces to the well-k nown result that the Moore-Penrose inverse of a boolean matrix, when i t exists, must be AT. (C) Elsevier Science Inc., 1997.