Weighted Moore-Penrose inverse of a Boolean matrix

Bapat, R. B. ; Jain, S. K. ; Pati, S. (1997) Weighted Moore-Penrose inverse of a Boolean matrix Linear Algebra and its Applications, 255 (1-3). pp. 267-279. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0024-3795(96)00777-X


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.

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