English

Vector spaces as unions of proper subspaces

Commutative Algebra 2015-02-02 v4 Combinatorics

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.

Keywords

Cite

@article{arxiv.0803.2746,
  title  = {Vector spaces as unions of proper subspaces},
  author = {Apoorva Khare},
  journal= {arXiv preprint arXiv:0803.2746},
  year   = {2015}
}

Comments

8 pages, LaTex; to appear in "Linear Algebra and its Applications"

R2 v1 2026-06-21T10:22:39.778Z