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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 $L+x$, where $x\in E$, is called a [[linear variety]] or linear manifold.

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How to Cite This Entry:
Linear subspace. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_subspace&oldid=55754

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article

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