Authors: Dinčić, Nebojša Č.
Đorđević, Bogdan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Yang-Baxter-Like Matrix Equation: A Road Less Taken
Series/Report no.: Mathematics Online First Collections
First page: 241
Last page: 346
Related Publication(s): Matrix and Operator Equations and Applications
Issue Date: 2023
Rank: M13
ISBN: 978-3-031-25385-0
DOI: 10.1007/16618_2023_49
This chapter represents a comprehensive analysis of the matrix equation AXA = XAX. We revise some of our published results regarding this topic and provide some new original unpublished results. In particular, we revisit our methods for constructing infinitely many nontrivial solutions, for both regular and singular matrix A, and we revisit our characterization of all permutation and doubly stochastic solutions when A is a permutation matrix. Additionally, we prove new results which concern the case when A is invertible: we obtain the closed-form formula for all commuting solutions and characterize the existence of non-commuting solutions (these conditions cannot be weakened). We also provide an alternative way for proving the existence of doubly stochastic solutions when A is a permutation matrix.
Keywords: Yang-Baxter-like matrix equation | Sylvester equation | Matrix functions
Publisher: Springer Link
Project: Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 451-03-68/2022-14/200029 and by the bilateral project between Serbia and Slovenia (Generalized inverses, operator equations and applications, Grant No. 337-00-21/2020-09/32)

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