Diagonalizable Quadratic Eigenvalue Problems

A system is defined to be an n× n matrix function L(λ) = λ2M + λD +K where M, D, K ∈ Cn×n and M is nonsingular. First, a careful review is made of the possibility of direct decoupling to a diagonal (real or complex) system by applying congruence or strict equivalence transformations to L(λ). However, the main contribution is a complete description of the much wider class of systems which can be decoupled by applying congruence or strict equivalence transformations to a linearization of a system while preserving the structure of L(λ). The theory is liberally illustrated with examples. A summary of canonical forms for diagonalizable systems is included as an Appendix.