Splitting a Linear System of Operator Equations With Constant Coefficients: a Matrix Polynomial Approach

Nikta Shayanfar, Mahmoud Hadizadeh

In this paper, we develop an efficient reduction technique that leads us to study particular classes of linear non-homogenous system of operator equations with constant coefficients. The key concept is assigning a matrix polynomial to the system, and its Smith canonical form provide a reduced system of independent equations. As a consequence of independent structure, each equation of the reduced system contains one unknown.