Algebraic proof methods for identities of matrices and operators: Improvements of Hartwig’s triple reverse order law

Dragana S. Cvetković-Ilić, Clemens Hofstadler, Jamal Hossein Poor, Jovana Milošević, Clemens G. Raab and Georg Regensburger

Applied Mathematics and Computation, 2021, vol. 409, issue C

Abstract: When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use Hartwig’s well-known triple reverse order law as an example for showing how this can be done using a recent framework for algebraic proofs and the software package OperatorGB. Our improvements of Hartwig’s result are proven in rings with involution and we discuss computer-assisted proofs that show these results in other settings based on the framework and a single computation with noncommutative polynomials.

Keywords: Matrices and linear operators; Algebraic operator identities; Generalized inverses; Reverse order law; Automated proofs; Noncommutative polynomials; Quiver representations (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:409:y:2021:i:c:s009630032100446x

DOI: 10.1016/j.amc.2021.126357

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