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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2003.06873 |
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| _version_ | 1866909172052787200 |
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| author | Acus, A. Dargys, A. |
| author_facet | Acus, A. Dargys, A. |
| contents | An algorithm to extract the square root in radicals from a multivector (MV) in real Clifford algebras Cl(p,q) for n=p+q <=3 is presented. We show that in the algebras Cl(3,0), Cl(1,2) and Cl(0,3) there are up to four isolated roots in a case of the most general (generic) MV. The algebra Cl(2,1) makes up an exception and the MV here can have up to 16 isolated roots. In addition to isolated roots, a continuum of roots can appear in all algebras except p+q=1. A number of examples are provided to illustrate properties of various roots that may appear in n=3 Clifford algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_06873 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Square root of a multivector of Clifford algebras in 3D: A game with signs Acus, A. Dargys, A. Mathematical Physics An algorithm to extract the square root in radicals from a multivector (MV) in real Clifford algebras Cl(p,q) for n=p+q <=3 is presented. We show that in the algebras Cl(3,0), Cl(1,2) and Cl(0,3) there are up to four isolated roots in a case of the most general (generic) MV. The algebra Cl(2,1) makes up an exception and the MV here can have up to 16 isolated roots. In addition to isolated roots, a continuum of roots can appear in all algebras except p+q=1. A number of examples are provided to illustrate properties of various roots that may appear in n=3 Clifford algebras. |
| title | Square root of a multivector of Clifford algebras in 3D: A game with signs |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2003.06873 |