Multivector (MV) functions in Clifford algebras of arbitrary dimension: Defective MV case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910908736864256 |
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| author | Acus, A. Dargys, A. |
| author_facet | Acus, A. Dargys, A. |
| contents | Explicit formulas to calculate MV functions in a basis-free representation are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on analysis of the roots of minimal MV polynomial and covers defective MVs, i.e. the MVs that have non-diagonalizable matrix representations. The method may be generalized straightforwardly to matrix functions and to finite dimensional linear operators. The results can find wide application in Clifford algebra analysis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_05730 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivector (MV) functions in Clifford algebras of arbitrary dimension: Defective MV case Acus, A. Dargys, A. Mathematical Physics 15A66, 15A67 Explicit formulas to calculate MV functions in a basis-free representation are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on analysis of the roots of minimal MV polynomial and covers defective MVs, i.e. the MVs that have non-diagonalizable matrix representations. The method may be generalized straightforwardly to matrix functions and to finite dimensional linear operators. The results can find wide application in Clifford algebra analysis. |
| title | Multivector (MV) functions in Clifford algebras of arbitrary dimension: Defective MV case |
| topic | Mathematical Physics 15A66, 15A67 |
| url | https://arxiv.org/abs/2412.05730 |