Hermitian Quadratic Matrix Polynomials: Solvents and Inverse Problems

Lancaster, Peter and Tisseur, Françoise (2010) Hermitian Quadratic Matrix Polynomials: Solvents and Inverse Problems. [MIMS Preprint]

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A monic quadratic Hermitian matrix polynomial $L(\lambda)$ can be factorized into a product of two linear matrix polynomials, say $L(\lambda)=(I\lambda-S)(I\lambda -A)$. For the inverse problem of finding a quadratic matrix polynomial with prescribed spectral data (eigenvalues and eigenvectors) it is natural to prescribe a right solvent $A$ and then determine compatible left solvents $S$. This problem is explored in the present paper. The splitting of the spectrum between real eigenvalues and nonreal conjugate pairs plays an important role. Special attention is paid to the case of real-symmetric quadratic polynomials.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
Depositing User: Dr Françoise Tisseur
Date Deposited: 12 Jan 2010
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1390

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