All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two. (18th June 2020)

• Record Type: Journal Article
• Authors: Zhou, Duanmei; Ding, Jiawen
• Other Names: Hafstein Sigurdur F. Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-06-18
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/2585602
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation A X A = X A X . We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.