Linear Equation over Non-Commutative Algebra

Abstract

I considered solving of the system of linear equations $$a_{1s0}^1{x}^1{a}_{1s1}^1+...+a_{ns0}^1{x}^n{a}_{ns1}^1=b^1$$ $$...$$ $$a_{1s0}^n{x}^1{a}_{1s1}^n+...+a_{ns0}^n{x}^n{a}_{ns1}^n=b^n$$ 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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