Primitive spaces of matrices of bounded rank. II
نویسندگان
چکیده
منابع مشابه
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...
متن کاملPrimitive Spaces of Matrices of Bounded Rank.ii
The classification of spaces of matrices of bounded rank is known to depend upon 'primitive' spaces, whose structure is considerably restricted. A characterisation of an infinite class of primitive spaces is given. The result is then applied to obtain a complete description of spaces whose matrices have rank at most 3. 1980 Mathematics subject classification (Amer. Math. Soc): 15 A 30, 15 A 03.
متن کاملSpaces 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...
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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...
متن کاملOn Spaces of Matrices Containing a Nonzero Matrix of Bounded Rank
Let Mn(R) and Sn(R) be the spaces of n × n real matrices and real symmetric matrices respectively. We continue to study d(n, n − 2,R): the minimal number such that every -dimensional subspace of Sn(R) contains a nonzero matrix of rank n−2 or less. We show that d(4, 2,R) = 5 and obtain some upper bounds and monotonicity properties of d(n, n − 2,R). We give upper bounds for the dimensions of n − ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1983
ISSN: 0263-6115
DOI: 10.1017/s1446788700023740