DIAGONALIZABLE QUADRATIC EIGENVALUE PROBLEMS

Abstract A system is defined to be an n × n matrix function L ( λ ) = λ 2 M + λ D + K where M , D , K ∈ C n × 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.

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