Abstract
The notion of standard triples plays a central role in the theory of matrix polynomials. We study such triples for matrix polynomials P(X) with structure S. where S is the Hermitian, symmetric, star-even, star-odd, star-palindromic or star-antipalindromic structure (with star = *, T). We introduce the notion of 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(X) has structure S if and only if P(lambda) admits an S-structured standard triple, and moreover that every standard triple of a matrix polynomial with structure S is S-structured. We investigate the important special case of S-structured Jordan triples. (C) 2012 Elsevier Inc. All rights reserved.