A local-global principle for linear dependence of noncommutative polynomials

Brešar, Matej; Klep, Igor

A local-global principle for linear dependence of noncommutative polynomials

Dateien

Tit283 Bresar.pdfGröße: 629.17 KBDownloads: 229

Datum

2011

Autor:innen

Brešar, Matej

Klep, Igor

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Noncommutative polynomial, free algebra, linear dependence, local linear dependence, polynomial identity, involution.

Zitieren

ISO 690

BREŠAR, Matej, Igor KLEP, 2011. A local-global principle for linear dependence of noncommutative polynomials

BibTex

@techreport{Bresar2011local-15280,
  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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