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==Field==
The next simplest example is the field '''F''' itself. Vector addition is just field addition and scalar multiplication is just field multiplication, and this property can be used to prove that field is a vector space. Any non-zero element of '''F''' serves as a basis so '''F''' is a 1-dimensional vector space over itself.
The field is a rather special vector space; in fact it is the simplest example of a '''[[algebra over a field|commutative algebra]]''' over '''F'''. Also, '''F''' has just two [[Linear subspace|subspaces]]: {0} and '''F''' itself.
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