Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation

Ashim Kumar, Dijana Mosić, Predrag S. Stanimirović, Gurjinder Singh and Lev A. Kazakovtsev
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Ashim Kumar: Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala 144603, India
Dijana Mosić: Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Predrag S. Stanimirović: Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Gurjinder Singh: Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala 144603, India
Lev A. Kazakovtsev: Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia

Mathematics, 2022, vol. 10, issue 15, 1-16

Abstract: This paper investigates new solution sets for the Yang–Baxter-like (YB-like) matrix equation involving constant entries or rational functional entries over complex numbers. Towards this aim, first, we introduce and characterize an essential class of generalized outer inverses (termed as { 2 , 5 } -inverses) of a matrix, which commute with it. This class of { 2 , 5 } -inverses is defined based on resolving appropriate matrix equations and inner inverses. In general, solutions to such matrix equations represent optimization problems and require the minimization of corresponding matrix norms. We decided to analytically extend the obtained results to the derivation of explicit formulae for solving the YB-like matrix equation. Furthermore, algorithms for computing the solutions are developed corresponding to the suggested methods in some computer algebra systems. The main features of the proposed approach are highlighted and illustrated by numerical experiments.

Keywords: Yang–Baxter-like matrix equation; outer inverse; Moore–Penrose inverse; idempotent matrices; computer algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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