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Volume 5, Issue 1
Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices

J. Ding & Noah H. Rhee

East Asian J. Appl. Math., 5 (2015), pp. 75-84.

Published online: 2018-02

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  • Abstract

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, where $A$ is any complex square matrix. A collection of spectral solutions for the unknown square matrix $X$ were previously found. When $A$ is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.

  • AMS Subject Headings

15A24, 47A35

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-75, author = {}, title = {Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {1}, pages = {75--84}, abstract = {

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, where $A$ is any complex square matrix. A collection of spectral solutions for the unknown square matrix $X$ were previously found. When $A$ is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.230414.311214a}, url = {http://global-sci.org/intro/article_detail/eajam/10780.html} }
TY - JOUR T1 - Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices JO - East Asian Journal on Applied Mathematics VL - 1 SP - 75 EP - 84 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.230414.311214a UR - https://global-sci.org/intro/article_detail/eajam/10780.html KW - Matrix equation, mean ergodic theorem, diagonalisable matrix. AB -

The Yang-Baxter-like matrix equation $AXA = XAX$ is reconsidered, where $A$ is any complex square matrix. A collection of spectral solutions for the unknown square matrix $X$ were previously found. When $A$ is diagonalisable, by applying the mean ergodic theorem we propose numerical methods to calculate those solutions.

J. Ding & Noah H. Rhee. (1970). Computing Solutions of the Yang-Baxter-Like Matrix Equation for Diagonalisable Matrices. East Asian Journal on Applied Mathematics. 5 (1). 75-84. doi:10.4208/eajam.230414.311214a
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