Publikation: A local-global principle for linear dependence of noncommutative polynomials
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2011
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Brešar, Matej
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Zusammenfassung
Abstract. A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a nite locally
linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the proof yields generalizations to rectional local linear dependence and evaluations in general algebras over elds of arbitrary characteristic. A main feature of the proof is that it makes it possible to deduce bounds on the size of the matrices where the (directional) local linear dependence needs to be tested in order to establish linear dependence.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Noncommutative polynomial, free algebra, linear dependence, local linear dependence, polynomial identity, involution.
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BREŠAR, Matej, Igor KLEP, 2011. A local-global principle for linear dependence of noncommutative polynomialsBibTex
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year={2011},
series={Konstanzer Schriften in Mathematik},
title={A local-global principle for linear dependence of noncommutative polynomials},
number={283},
author={Brešar, Matej and Klep, Igor}
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