Diagonalizable quadratic eigenvalue problems

A system is defined to be an n×nn×n matrix function L(λ)=λ2M+λD+KL(λ)=λ2M+λD+K where M,D,K∈Cn×nM,D,K∈Cn×n and MM 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)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)L(λ). The theory is liberally illustrated with examples.