Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices
We prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2014-02-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/spma-2014-0002 |
| _version_ | 1819291044506763264 |
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| author | Macías-Virgós E. Pereira-Sáez M.J. |
| author_facet | Macías-Virgós E. Pereira-Sáez M.J. |
| author_sort | Macías-Virgós E. |
| collection | DOAJ |
| description | We prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem. |
| first_indexed | 2024-12-24T03:32:23Z |
| format | Article |
| id | doaj.art-6e8d08af42004844b07e430e9906bb40 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-24T03:32:23Z |
| publishDate | 2014-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-6e8d08af42004844b07e430e9906bb402022-12-21T17:17:09ZengDe GruyterSpecial Matrices2300-74512014-02-012110.2478/spma-2014-0002spma-2014-0002Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matricesMacías-Virgós E.0Pereira-Sáez M.J.1Facultade de Matemáticas, Universidade de Santiago de Compostela, SpainFacultade de Economía e Empresa, Universidade da Coruña, SpainWe prove that any quaternionic matrix of order n ≤3 admits a characteristic function, whose roots are the left eigenvalues, that satisfes Cayley-Hamilton theorem.https://doi.org/10.2478/spma-2014-0002quaternionic matrixleft eigenvaluecharacteristic functioncayley-hamilton theorem |
| spellingShingle | Macías-Virgós E. Pereira-Sáez M.J. Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices Special Matrices quaternionic matrix left eigenvalue characteristic function cayley-hamilton theorem |
| title | Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices |
| title_full | Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices |
| title_fullStr | Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices |
| title_full_unstemmed | Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices |
| title_short | Cayley-Hamilton theorem for left eigenvalues of 3 × 3 quaternionic matrices |
| title_sort | cayley hamilton theorem for left eigenvalues of 3 3 quaternionic matrices |
| topic | quaternionic matrix left eigenvalue characteristic function cayley-hamilton theorem |
| url | https://doi.org/10.2478/spma-2014-0002 |
| work_keys_str_mv | AT maciasvirgose cayleyhamiltontheoremforlefteigenvaluesof33quaternionicmatrices AT pereirasaezmj cayleyhamiltontheoremforlefteigenvaluesof33quaternionicmatrices |