East Asian J. Appl. Math., 3 (2013), pp. 352-362.
Published online: 2018-02
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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} }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.