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arXiv · 2403.17965

Linear Equation over Non-Commutative Algebra

Aleks Kleyn
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Abstract

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.

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Aleks Kleyn. 2024-03-15. Linear Equation over Non-Commutative Algebra. https://doi.org/10.1007/s11785-025-01706-6

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