Duality of matrix pencils and linearizations

Noferini, Vanni and Poloni, Federico (2013) Duality of matrix pencils and linearizations. [MIMS Preprint]

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Abstract

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 L1, L2 linearization spaces are strong linearizations, a new perspective on Fiedler pencils, a link between the Möller-Stetter theorem and some linearizations of matrix polynomials.

Item Type: MIMS Preprint
Uncontrolled Keywords: matrix pencil, Wong chain, linearization, matrix polynomial, singular pencil, Fiedler pencil, pencil duality, Kronecker canonical form
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
Depositing User: Dr V Noferini
Date Deposited: 22 Apr 2013
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1968

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