Linear Equation over Non-Commutative Algebra

2024/03/15 by Kleyn, Aleks
#FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2403.17965

Abstract

I considered solving of the system of linear equations a¹_1s0x¹a¹_1s1+...+a¹_ns0xⁿa¹_ns1=b¹ ... aⁿ_1s0x¹aⁿ_1s1+...+aⁿ_ns0xⁿaⁿ_ns1=bⁿ 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.

Related

• A note on polynomial equations over algebras
• Linear Equation in Finite Dimensional Algebra
• Quadratic Equation over Associative D-Algebra
• Introduction into Noncommutative Algebra, Volume 1
• Two Non-Commutative Binomial Theorems