Maximal rank-one spaces of matrices over chain semirings. II. (u, i)-spaces

Spaces of rank-2 matrices over GF(2)

The possible dimensions of spaces of matrices over GF(2) whose nonzero elements all have rank 2 are investigated.

Primitive Spaces of Matrices of Bounded Rank

A weak canonical form is derived for vector spaces of m x n matrices all of rank at most r. This shows that the structure of such spaces is controlled by the structure of an associated 'primitive' space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight. 1980 Mathematics subject classification (Amer. Math. Soc.): 15 A 30, 15 A...

Vector Spaces of Matrices of Low Rank

In this paper we study vector spaces of matrices, all of whose elements have rank at most a given number. The problem of classifying such spaces is roughly equivalent to the problem of classifying certain torsion-free sheaves on projective spaces. We solve this problem in case the sheaf in question has first Chern class equal to 1; the characterization of the vector spaces of matrices of rank d...

Spaces of Matrices of Bounded Rank

IN this paper we shall consider matrices over a field F and shall prove the following result: THEOREM. Let M be a 2-dimensional space o/mxn matrices with the property that rank (X) *£ k < \F\ for every XeM. Then there exist two integers r, s, O^r, s *£ fc with r + s = k, and two non-singular matrices P, Q such that, for all XeM, PXQ has the form Notice that a matrix of the above form necessaril...

Rank One Maximal Cohen-macaulay Modules Over