Rational matrix solutions to the Leech equation: The Ball-Trent approach revisited

TL;DR

This paper revisits the Ball-Trent approach to explicitly compute rational matrix solutions for the Leech equation using spectral factorization, extending previous polynomial-based methods to rational data.

Contribution

It generalizes the Ball-Trent method to rational matrix data, providing an explicit spectral factorization-based solution for the Leech equation.

Findings

Provides an explicit spectral factorization method for rational solutions

Extends previous polynomial techniques to rational matrix data

Enables practical computation of solutions for the Leech equation

Abstract

Using spectral factorization techniques, a method is given by which rational matrix solutions to the Leech equation with rational matrix data can be computed explicitly. This method is based on an approach by J.A. Ball and T.T. Trent, and generalizes techniques from recent work of T.T. Trent for the case of polynomial matrix data.