, Volume 9, Issue 4, pp 393-395

A nowhere-zero point in linear mappings

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Abstract

We state the following conjecture and prove it for the case whereq is a proper prime power:

Let A be a nonsingular n by n matrix over the finite field GFqq≧4, then there exists a vector x in (GFq)n such that both x and Ax have no zero component.

Research supported in part by Allon Fellowship and by a Bat Sheva de Rothschild grant.