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Block generalized inverses

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Abstract

The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring R. A technique is developed for computing conditional and reflexive inverses for matrices in R2×2, which is then used to calculate the Moore-Penrose inverse for these matrices. Several applications are given, generalizing many of the classical results; in particular, we shall emphasize the cases of bordered matrices, Schur complements, block-rank formulae and EP elements.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 27607, Raleigh, N.C.

    Robert E. Hartwig

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  1. Robert E. Hartwig
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Communicated by M. Kac

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Hartwig, R.E. Block generalized inverses. Arch. Rational Mech. Anal. 61, 197–251 (1976). https://doi.org/10.1007/BF00281485

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