On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation - Yunbo Tian; Chao Xia (Journal of Mathematics)
We study the low-degree solution of the Sylvester matrix equation A1λ+A0Xλ+YλB1λ+B0=C0, where A1λ+A0 and B1λ+B0 are regular. Using the substitution of parameter variables λ, we assume that the matrices A0 and B0 are invertible. Thus, we prove that if the equation is solvable, then it has a low-degree solution Lλ,Mλ, satisfying the degree conditions δLλ<IndA0−1A1 and δMλ<IndB1B0−1.