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The generalized Moore-Penrose inverse. (English) Zbl 0743.15007
The generalized Moore-Penrose inverse of a matrix over an integral domain with involution is defined. Necessary and sufficient conditions for the existence of this inverse are given. Uniqueness is proven and a formula given which leads toward a “generalized Cramer’s rule” to find the generalized Moore-Penrose solution.

MSC:
15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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[1] R.B. Bapat, K.P.S. Bhaskara Rao, and K. Manjunatha Prasad, Generalized inverses over integral domians, to appear.
[2] Ben-Israel, A.; Greville, T.N.E., Generalized inverses and applications, (1974), Wiley · Zbl 0305.15001
[3] Bhaskara Rao, K.P.S., On generalized inverses of matrices over integral domians, Linear algebra appl., 49, 179-189, (1983) · Zbl 0505.15002
[4] Puystjens, R.; Robinson, D.W., The Moore-Penrose inverse of a morphism in an additive category, Comm. algebra, 12, 3, 287-299, (1984) · Zbl 0534.18004
[5] Rao, C.R.; Mitra, S.K., Generalized inverse of matrices and applications, (1974), Wiley
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