Vector spaces as unions of proper subspaces
arXiv:0803.2746 · doi:10.1016/j.laa.2009.06.001
Abstract
In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of partitioning V into subspaces.
8 pages, LaTex; to appear in "Linear Algebra and its Applications"
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