Algebraic systems of matrices and Grobner basis

TL;DR

This paper explores algebraic systems involving matrices and demonstrates how Grobner basis theory can be used to solve these systems based on parameter values.

Contribution

It introduces a method for solving matrix-based algebraic systems using Grobner basis theory, highlighting a novel application of algebraic techniques.

Findings

Solution method for matrix algebraic systems using Grobner basis

Parameter-dependent solutions for matrix systems

Application of algebraic geometry to matrix equations

Abstract

One studies a particular algebraic system where the unknowns are matrices. We solve this system according to the parameters values thanks to the theory of Grobner basis.