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Dimension
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===Vector spaces=== {{Main|Dimension (vector space)}} The dimension of a [[vector space]] is the number of vectors in any [[Basis (linear algebra)|basis]] for the space, [[Id est|i.e.]] the number of coordinates necessary to specify any vector. This notion of dimension (the [[cardinality]] of a basis) is often referred to as the ''Hamel dimension'' or ''algebraic dimension'' to distinguish it from other notions of dimension. For the non-[[free module|free]] case, this generalizes to the notion of the [[length of a module]].
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