SPLITTING A LINEAR SYSTEM OF OPERATOR EQUATIONS INTO INDEPENDENT EQUATIONS BY MATRIX POLYNOMIALS

In this paper, we present an algorithm for splitting a linear system of operator equations into a class of independent equations. Considering an appropriate operator as the variable of the matrix polynomial, a matrix polynomial equation corresponding to the operator system is determined. The Smith decomposition of the matrix polynomial, enables us to characterize a class of independent equations consist of higher order linear operator equations having only one variable