Formulae of Partial Reduction for Linear Systems of First Order Operator Equations

TL;DR

This paper presents a method to reduce non-homogeneous linear systems of first order operator equations with constant coefficients into simpler forms using rational canonical form, facilitating easier analysis and solution.

Contribution

It introduces a novel reduction technique transforming complex systems into higher order and two-variable equations via rational canonical form.

Findings

Reduction simplifies solving linear operator systems.

Equivalent systems are obtained with higher order and two-variable equations.

Method enhances analytical tractability of linear operator systems.

Abstract

This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and first order linear operator equations in two variables, is obtained by using the rational canonical form.