Linear subspace

One-dimensional subspaces in the two-dimensional vector space over the finite field F5. The origin (0, 0), marked with green circles, belongs to any of six 1-subspaces, while each of 24 remaining points belongs to exactly one; a property which holds for 1-subspaces over any field and in all dimensions. All F52 (i.e. a 5 × 5 square) is pictured four times for a better visualization

In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace^{[1][note 1]} is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.

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