Duality of matrix pencils and linearizations
Vanni Noferini, Federico Poloni · MIMS EPrints (University of Southampton) · 2013
In this paper we introduce a duality relation on matrix pencils and show that it is a useful tool in the theory of linearizations of matrix polynomials.We first completely characterize the Kronecker form of dual pencils.Exploiting this result, we then study the behaviour under duality of the spectral structures, including eigenvalues, eigenvectors, Wong chains, and minimal bases.We also present several applications of the new concept, including: constraints on the minimal indices of singular Hamiltonian and symplectic pencils, new sufficient conditions under which pencils in L 1 , L 2 linearization spaces are strong linearizations, a new perspective on Fiedler pencils, a link between the Möller-Stetter theorem and some linearizations of matrix polynomials.