A Short Note on the Reduction Formulas for Some Systems of Linear Operator Equations

Abstract

We consider partial and total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the same particular form as in paper [7]. Here we present two different concepts, one is concerned with partially reduced systems obtained by using the Jordan and the rational form of the system matrix. The other one is dealing with totally reduced systems obtained by finding the adjugate matrix of the characteristic matrix of the system matrix.