Weighted Moore-Penrose inverse of a boolean matrix Original Research Article

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 satisfies 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 inverse exists if and only if ANATMA = A, in which case the inverse is NTATMT. When M, N are identity matrices, this reduces to the well-known result that the Moore-Penrose inverse of a boolean matrix, when it exists, must be AT.