Title

Solving the Yang-Baxter-like Matrix Equation for a Class of Elementary Matrices

Document Type

Article

Publication Date

9-2016

Department

Mathematics

Abstract

Let u and v be two n-dimensional vectors in the complex field such that v(T)u not equal 0, and let A = I - uv(T). We find all the solutions of the quadratic matrix equation AXA = XAX in various situations, with the help of a spectral perturbation result for rank-one updated matrices. Two numerical examples are given to demonstrate the effectiveness of the method, including an application of the result to a 4 x 4 equation related to the classic Yang-Baxter equation. (C) 2016 Elsevier Ltd. All rights reserved.

Publication Title

Computers and Mathematics with Applications

Volume

72

Issue

6

First Page

338

Last Page

343

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