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Weighted Moore-Penrose inverse of a boolean matrix

✍ Scribed by R.B. Bapat; S.K. Jain; S. Pati

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
609 KB
Volume
255
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 NTATM T. 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. 0

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