All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2585602 |
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| _version_ | 1832554082724741120 |
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| author | Duanmei Zhou Jiawen Ding |
| author_facet | Duanmei Zhou Jiawen Ding |
| author_sort | Duanmei Zhou |
| collection | DOAJ |
| description | Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation. |
| format | Article |
| id | doaj-art-579a85e7a7ae4877a4484de93f9ae614 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-579a85e7a7ae4877a4484de93f9ae6142025-02-03T05:52:27ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/25856022585602All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index TwoDuanmei Zhou0Jiawen Ding1College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, ChinaCollege of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, ChinaLet A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.http://dx.doi.org/10.1155/2020/2585602 |
| spellingShingle | Duanmei Zhou Jiawen Ding All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two Complexity |
| title | All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two |
| title_full | All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two |
| title_fullStr | All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two |
| title_full_unstemmed | All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two |
| title_short | All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two |
| title_sort | all solutions of the yang baxter like matrix equation for nilpotent matrices of index two |
| url | http://dx.doi.org/10.1155/2020/2585602 |
| work_keys_str_mv | AT duanmeizhou allsolutionsoftheyangbaxterlikematrixequationfornilpotentmatricesofindextwo AT jiawending allsolutionsoftheyangbaxterlikematrixequationfornilpotentmatricesofindextwo |