Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912585026109440 |
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| author | Tajima, Shinichi Ohara, Katsuyoshi Terui, Akira |
| author_facet | Tajima, Shinichi Ohara, Katsuyoshi Terui, Akira |
| contents | An effective exact method is proposed for computing generalized eigenspaces of a matrix of integers or rational numbers. Keys of our approach are the use of minimal annihilating polynomials and the concept of the Jourdan-Krylov basis. A new method, called Jordan-Krylov elimination, is introduced to design an algorithm for computing Jordan-Krylov basis. The resulting algorithm outputs generalized eigenspaces as a form of Jordan chains. Notably, in the output, components of generalized eigenvectors are expressed as polynomials in the associated eigenvalue as a variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04807 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis Tajima, Shinichi Ohara, Katsuyoshi Terui, Akira Rings and Algebras Symbolic Computation Commutative Algebra 15A18, 68W30 An effective exact method is proposed for computing generalized eigenspaces of a matrix of integers or rational numbers. Keys of our approach are the use of minimal annihilating polynomials and the concept of the Jourdan-Krylov basis. A new method, called Jordan-Krylov elimination, is introduced to design an algorithm for computing Jordan-Krylov basis. The resulting algorithm outputs generalized eigenspaces as a form of Jordan chains. Notably, in the output, components of generalized eigenvectors are expressed as polynomials in the associated eigenvalue as a variable. |
| title | Exact Algorithms for Computing Generalized Eigenspaces of Matrices via Jordan-Krylov Basis |
| topic | Rings and Algebras Symbolic Computation Commutative Algebra 15A18, 68W30 |
| url | https://arxiv.org/abs/2209.04807 |