Year: 2013
Type: preprint
Abstract: An n\times n matrix M is called a fooling-set matrix of size n, if its diagonal entries are nonzero, whereas for every k\ne \ell we have M_{k,\ell} M_{\ell,k} = 0. Dietzfelbinger, Hromkovič, and Schnitger (1996) showed that n \le (\rk M)^2, regardless of over which field the rank is computed, and asked whether the exponent on \rk M can be improved. We settle this question for nonzero characteristic by constructing a family of matrices for which the bound is asymptotically tight. The construction uses linear recurring sequences.
Source: arXiv (Cornell University)
Authors: Friesen, Mirjam, Theis, Dirk Oliver
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1566852934