Linear Equation over Non-Commutative Algebra
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915532122357760 |
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| author | Kleyn, Aleks |
| author_facet | Kleyn, Aleks |
| contents | I considered solving of the system of linear equations $$a^1_{1s0}x^1a^1_{1s1}+...+a^1_{ns0}x^na^1_{ns1}=b^1$$ $$...$$ $$a^n_{1s0}x^1a^n_{1s1}+...+a^n_{ns0}x^na^n_{ns1}=b^n$$ over non-commutative associative algebra. I considered examples in quaternion algebra. I considered also Newton's method to solve the equation $$f(x)=a$$ over non-commutative associative algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear Equation over Non-Commutative Algebra Kleyn, Aleks General Mathematics I considered solving of the system of linear equations $$a^1_{1s0}x^1a^1_{1s1}+...+a^1_{ns0}x^na^1_{ns1}=b^1$$ $$...$$ $$a^n_{1s0}x^1a^n_{1s1}+...+a^n_{ns0}x^na^n_{ns1}=b^n$$ over non-commutative associative algebra. I considered examples in quaternion algebra. I considered also Newton's method to solve the equation $$f(x)=a$$ over non-commutative associative algebra. |
| title | Linear Equation over Non-Commutative Algebra |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2403.17965 |