Large spaces of bounded rank matrices revisited
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 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...
متن کاملLARGE SPACES OF MATRICES OF BOUNDED RANK By M. D. ATKINSON and S. LLOYD
IN THIS paper we consider subspaces X of M^*, the space of all m x n matrices with entries in some given field, with the property that each matrix of X has rank at most r. In [2] Flanders showed that such spaces necessarily have dimension at most max (mr, nr) and he determined the spaces of precisely this dimension. We shall extend this work by classifying the spaces of dimension slightly lower...
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 کاملVector 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.051