Triangularizing matrix polynomials

Taslaman, Leo and Tisseur, Francoise and Zaballa, Ion (2012) Triangularizing matrix polynomials. [MIMS Preprint]

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Abstract

For an algebraically closed field $\F$, we show that any matrix polynomial $P(\lambda)\in \F[\lambda]^{\nbym}$, $n\le m$, can be reduced to triangular form, preserving the degree and the finite and infinite elementary divisors. We also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes $1\times 1$ and $2 \times 2$. The proofs we present solve the structured inverse problem of building up triangular matrix polynomials starting from lists of elementary divisors.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Fran├žoise Tisseur
Date Deposited: 02 Nov 2012
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1908

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