Search results for "Locally linearly dependent"

MR3038546, Brešar, Matej; Klep, Igor A local-global principle for linear dependence of noncommutative polynomials. Israel J. Math. 193 (2013), no. 1,…

2014

Let F be a eld of characteristic zero and FhXi the free associative algebra on X = fX1;X2; : : : g over F; i.e., the algebra of polynomials in the non-commuting variables Xi 2 X. A set of polynomials in FhXi is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. In [Integral Equations Operator Theory 46 (2003), no. 4, 399{454; MR1997979 (2004f:90102)], J. F. Camino et al., in the setting of free analysis, motivated by systems engineering, proved that a nite locally linearly dependent set of polynomials is linearly dependent. In this paper the authors give an alternative algebraic proof of this result based on the theory of polynomial i…