Volume 3, Issue 4
Further Solutions of a Yang-Baxter-Like Matrix Equation

East Asian J. Appl. Math., 3 (2013), pp. 352-362.

Published online: 2018-02

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• Abstract

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, and an infinite number of solutions that commute with any given complex square matrix A are found. Our results here are based on the fact that the matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.

• Keywords

Matrix equation, Jordan canonical form, projector.

15A18

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@Article{EAJAM-3-352, author = {}, title = {Further Solutions of a Yang-Baxter-Like Matrix Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {4}, pages = {352--362}, abstract = {

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, and an infinite number of solutions that commute with any given complex square matrix A are found. Our results here are based on the fact that the matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130713.221113a}, url = {http://global-sci.org/intro/article_detail/eajam/10862.html} }
TY - JOUR T1 - Further Solutions of a Yang-Baxter-Like Matrix Equation JO - East Asian Journal on Applied Mathematics VL - 4 SP - 352 EP - 362 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.130713.221113a UR - https://global-sci.org/intro/article_detail/eajam/10862.html KW - Matrix equation, Jordan canonical form, projector. AB -

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, and an infinite number of solutions that commute with any given complex square matrix A are found. Our results here are based on the fact that the matrix A can be replaced with its Jordan canonical form. We also discuss the explicit structure of the solutions obtained.

Jiu Ding, Chenhua Zhang & Noah H. Rhee. (1970). Further Solutions of a Yang-Baxter-Like Matrix Equation. East Asian Journal on Applied Mathematics. 3 (4). 352-362. doi:10.4208/eajam.130713.221113a
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