Linear subspace

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vector subspace

A non-empty subset $L$ of a (linear) vector space $E$ over a field $K$ such that $L$ itself is a vector space with respect to the operations of addition and multiplication by a scalar defined in $E$. A set $L+x_0$, where $x_0\in E$, is called a linear variety or linear manifold.

How to Cite This Entry:
Linear subspace. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article