Standard Triples of Structured Matrix Polynomials

Al-Ammari, Maha and Tisseur, Francoise (2011) Standard Triples of Structured Matrix Polynomials. [MIMS Preprint]

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Abstract

The notion of standard triples plays a central role in the theory of matrix polynomials. We study such triples for matrix polynomials $P(\lambda)$ with structure $\mathcal{S}$, where $\mathcal{S}$ is the Hermitian, symmetric, $\star$-even, $\star$-odd, $\star$-palindromic or $\star$-antipalindromic structure (with $\star=*,T$). We introduce the notion of $\mathcal{S}$-structured standard triple. With the exception of $T$-(anti)palindromic matrix polynomials of even degree with both $-1$ and $1$ as eigenvalues, we show that $P(\lambda)$ has structure $\mathcal{S}$ if and only if $P(\lambda)$ admits an $\mathcal{S}$-structured standard triple, and moreover that every standard triple of a matrix polynomial with structure $\mathcal{S}$ is $\mathcal{S}$-structured. We investigate the important special case of $\mathcal{S}$-structured Jordan triples.

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 Françoise Tisseur
Date Deposited:	11 Jan 2012
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1753

Available Versions of this Item

• Standard Triples of Structured Matrix Polynomials. (deposited 10 May 2011)
  • Standard Triples of Structured Matrix Polynomials. (deposited 11 Jan 2012) [Currently Displayed]

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