Automatically assigned DDC number:
Manually assigned DDC number: 5199434
Title: Spaces Of Rank-2 Matrices Over Gf(2)
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 , , . In , , it was shown that the dimension of a rank-k space is at most n + m Gamma 2k + 1, and in  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  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...
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