Covering Numbers in Linear Algebra
Pete L. Clark
TL;DR
This paper determines the smallest number of proper linear subspaces needed to cover a vector space over any field, including affine subspaces, providing fundamental insights into linear algebra coverings.
Contribution
It introduces formulas for minimal covering numbers of vector spaces and affine spaces by proper subspaces over arbitrary fields, extending previous results.
Findings
Computed minimal covering cardinalities for vector spaces over arbitrary fields
Extended results to affine linear subspace coverings
Provided formulas for irredundant coverings
Abstract
We compute the minimal cardinality of a covering (resp. an irredundant covering) of a vector space over an arbitrary field by proper linear subspaces. Analogues for affine linear subspaces are also given.
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Taxonomy
TopicsRings, Modules, and Algebras · Polynomial and algebraic computation · Advanced Topics in Algebra