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Keywords

Ring, outer inverse, Bott-Duffin-inverse, {1, 3}-inverse, {1, 4}-inverse, Moore-Penrose inverse

Abstract

Let R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a in R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications to block matrices over a ring are given.

abs_vol_30_pp118-134.pdf (27 kB)
Abstract

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