AlAmmari, 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 
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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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