Prime decomposition of quadratic matrix polynomials

Abstract

We study the prime decomposition of a quadratic monic matrix polynomial. From the prime decomposition of a quadratic matrix polynomial, we obtain a formula of the general solution to the corresponding second-order differential equation. For a quadratic matrix polynomial with pairwise commuting coefficients, we get a sufficient condition for the existence of a prime decomposition.

Keywords

• differential equation
• matrix polynomials
• factorization
• matrix equation
• matrix pencil
• explicit solution