Extension of the Fundamental Theorem of Algebra for Polynomial Matrix Equations with Circulant Matrices

TL;DR

This paper extends the fundamental theorem of algebra to polynomial matrix equations where both the coefficients and unknowns are circulant matrices, broadening algebraic understanding in matrix polynomial contexts.

Contribution

It introduces an analogue of the fundamental theorem of algebra specifically for polynomial equations involving circulant matrices, a novel extension in matrix algebra.

Findings

Established an algebraic analogue for circulant matrix polynomial equations

Provided theoretical foundations for solving such matrix equations

Enhanced understanding of polynomial matrix equations with circulant structures

Abstract

We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.