Zero-degree solutions to the bilateral polynomial matrix equations
The paper deals with the bilateral polynomial matrix equation \(AX+YB=C\) and, for given A, B, C, with the following two problems: 1. Find X, Y such that deg X\(=0\) and deg Y\(=0\); 2. Find X, Y such that deg X\(=0\) and deg \(Y\leq \max (\deg A\), deg C) - deg B. Necessary and sufficient conditions for the existence of the solutions are respectively proved. For problem 2 an illustrative example is given.
scientific article; zbMATH DE number 3983387