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This page lists some '''examples of vector spaces'''. See [[vector space]] for the definitions of terms used on this page. See also: [[dimension (vector space)|dimension]], [[basis (linear algebra)|basis]].
''Notation''. We will let '''F''' denote an arbitrary [[field (mathematics)|field]] such as the [[real number]]s '''R''' or the [[complex number]]s '''C'''
==Trivial or zero vector space==
The simplest example of a vector space is the trivial one: {'''0'''}, which contains only the zero vector (see axiom 3 of [[vector space]]s). Both vector addition and scalar multiplication are trivial. A [[basis (linear algebra)|basis]] for this vector space is the [[empty set]], so that {0} is the 0-dimensional vector space over '''F'''. Every vector space over '''F''' contains a subspace [[Isomorphism|isomorphic]] to this one.
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