We state the following conjecture and prove it for the case where q 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.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Computational Mathematics
- AMS subject classifications (1980): 05B35, 05B25, 12C05