Structured Multi-Matrix Variate, Matrix Polynomial Equations: Solution Techniques

TL;DR

This paper develops solution techniques for structured multi-matrix variate polynomial equations, including eigenvalue determination and diagonalization methods, with potential implications for non-commutative algebra.

Contribution

It introduces new lemmas and methods for solving multi-matrix variate polynomial equations and generalizes these results to tensor variate equations.

Findings

Eigenvalue determination lemmas proved

Diagonalization methods for unknown matrices provided

Generalization to tensor variate polynomial equations discussed

Abstract

In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown matrices is provided. The results are generalized to multi-matrix variate, matrix polynomial equations. Briefly generalization to tensor variate polynomial equations is discussed. It is hoped that the results lead to important contributions in "non-commutative algebra".