naa a22 4500 510782469 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s11856-012-0066-4 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0066-4 A local-global principle for linear dependence of noncommutative polynomials [Elektronische Daten] [Matej Brešar, Igor Klep] 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 finite 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 directional local linear dependence and evaluations in general algebras over fields 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. Hebrew University Magnes Press, 2012 Brešar Matej Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1111, Ljubljana, Slovenia aut Klep Igor Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1111, Ljubljana, Slovenia aut Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 71-82 0021-2172 193:1<71 2013 193 11856 https://doi.org/10.1007/s11856-012-0066-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0066-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brešar Matej Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1111, Ljubljana, Slovenia aut NATIONALLICENCE 700 1- Klep Igor Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, SI-1111, Ljubljana, Slovenia aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 71-82 0021-2172 193:1<71 2013 193 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer