Solving the Yang-Baxter-Like Matrix Equation With Non-Diagonalizable Elementary Matrices

Authors

Duanmei Zhou, Gannan Normal UniversityFollow
Guoliang Chen, East China Normal UniversityFollow
Jiu Ding, University of Southern MississippiFollow
Haiyan Tian, University of Southern MississippiFollow

Document Type

Article

Publication Date

1-1-2019

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Let A = I − uv^t, where u and v are two n-dimensional complex vectors with v^tu = 0. Thus A is not diagonalizable. We find all solutions of the quadratic matrix equation AXA = XAX. This is a continuation of the work [Compters Math. Appl., 72(6):1541-1548, 2016] from the case of diagonalizable elementary matrices to non-diagonalizable ones.

Publication Title

Communications in Mathematical Sciences

Volume

17

Issue

2

First Page

393

Last Page

411

Recommended Citation

Zhou, D., Chen, G., Ding, J., Tian, H. (2019). Solving the Yang-Baxter-Like Matrix Equation With Non-Diagonalizable Elementary Matrices. Communications in Mathematical Sciences, 17(2), 393-411.
Available at: https://aquila.usm.edu/fac_pubs/16960