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

Описание

Тип публикации: статья из журнала

Год издания: 2022

Идентификатор DOI: 10.3390/math10152738

Ключевые слова: computer algebra, idempotent matrices, moore–penrose inverse, outer inverse, yang–baxter-like matrix equation

Аннотация: 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 (Formula presented.) -inverses) of a matrix, Показать полностьюwhich commute with it. This class of (Formula presented.) -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. © 2022 by the authors.

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Издание

Журнал: Mathematics

Выпуск журнала: Vol. 10, Is. 15

Номера страниц: 2738

ISSN журнала: 22277390

Издатель: MDPI

Персоны

  • Kumar A. (Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala, 144603, India)
  • Mosić D. (Faculty of Sciences and Mathematics, University of Niš, Niš, 18000, Serbia)
  • Stanimirović P.S. (Faculty of Sciences and Mathematics, University of Niš, Niš, 18000, Serbia, Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk, 660041, Russian Federation)
  • Singh G. (Department of Mathematical Sciences, I.K. Gujral Punjab Technical University Jalandhar, Kapurthala, 144603, India)
  • Kazakovtsev L.A. (Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk, 660041, Russian Federation)

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