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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.07980 |
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| _version_ | 1866929752720277504 |
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| author | Zhang, Haicheng Zhu, Xiyan |
| author_facet | Zhang, Haicheng Zhu, Xiyan |
| contents | We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices under similarity. As an application, we determine the eigenvalues and eigenspaces of pseudo-diagonalizable matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A similarity canonical form for max-plus matrices and its eigenproblem Zhang, Haicheng Zhu, Xiyan Rings and Algebras We provide a necessary and sufficient condition for matrices in the max-plus algebra to be pseudo-diagonalizable, calculate the powers of pseudo-diagonal matrices and prove the invariance of optimal-node matrices and separable matrices under similarity. As an application, we determine the eigenvalues and eigenspaces of pseudo-diagonalizable matrices. |
| title | A similarity canonical form for max-plus matrices and its eigenproblem |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2503.07980 |