Automatically assigned DDC number:

Manually assigned DDC number: 5199434

Title: Spaces Of Rank-2 Matrices Over Gf(2)

Author:

Subject: Leroy B. Beasley Spaces Of Rank-2 Matrices Over Gf(2)

Description: . The possible dimensions of spaces of matrices over GF(2) whose nonzero elements all have rank 2 are investigated. Key words. Matrix, rank, rank-k space. AMS subject classifications. 15A03, 15A33, 11T35 Let Mm;n (F ) denote the vector space of all m Theta n matrices over the field F . In the case that m = n we write Mn (F ). A subspace, K, is called a rank-k space if each nonzero entry in K has rank equal k. We assume throughout that 1 k m n. The structure of rank-k spaces has been studied lately by not only matrix theorists but group theorists and algebraic geometers; see [4], [5], [6]. In [3], [7], it was shown that the dimension of a rank-k space is at most n + m Gamma 2k + 1, and in [1] that the dimension of a rank-k space is at most max(k + 1; n Gamma k + 1), when the field is algebraically closed. In [2] it was shown that, if jF j n + 1 and n 2k Gamma 1, then the dimension of a rank-k space is at most n. Thus, if k = 2 and F is not the field of two elements, we know...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1999-02-03

Pubyear: unknown

Format: ps

Identifier: http://citeseer.ist.psu.edu/140049.html

Source: http://math.usu.edu/~lbeasley/papers/vol5_pp11-18.ps

Language: en

Rights: unrestricted