| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 26, Number 6, December 2021
|
|
|---|---|---|
| Page(s) | 459 - 463 | |
| DOI | https://doi.org/10.1051/wujns/2021266459 | |
| Published online | 17 December 2021 | |
Mathematics
CLC number: O124.6
Some Rank Formulas for the Yang-Baxter Matrix Equation AXA = XAX
School of Mathematics and Statistics, Tianshui Normal University, Tianshui
741001, Gansu, China
† To whom correspondence should be addressed. E-mail: liangml2005@163.com; liangmaolin@tsnu.edu.cn
Received:
20
July
2021
Let A be an arbitrary square matrix, then equation AXA =XAX with unknown X is called Yang-Baxter matrix equation. It is difficult to find all the solutions of this equation for any given A. In this paper, the relations between the matrices A and B are established via solving the associated rank optimization problem, where B =AXA = XAX, and some analytical formulas are derived, which may be useful for finding all the solutions and analyzing the structures of the solutions of the above Yang-Baxter matrix equation.
Key words: Yang-Baxter matrix equation / rank / generalized inverse
Biography: DAI Lifang, female, Master, research direction: numerical linear algebra with applications. E-mail: dailf2005@163.com
Foundation item: Supported by the National Natural Science Foundation of China (11961057) , the Science and Technology Project of Gansu Province ( 21JR1RE287 and 2021B-221) , the Fuxi Scientific Research Innovation Team of Tianshui Normal University (FXD2020-03) , and the Science Foundation ( CXT2019-36 and CXJ2020-11) as well as the Education and Teaching Reform Project of Tianshui Normal University ( JY202004 and JY203008)
© Wuhan University 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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