Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. All bases of a vector space have equal cardinality (see dimension theorem for vector spaces) and so the dimension of a vector space is uniquely defined. The dimension of the vector space V over the field F is written as dimF(V).

Related Topics:
Mathematics - Vector space - Cardinality - Basis - Dimension - Dimension theorem for vector spaces - Field

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We say V is finite-dimensional if the dimension of V is finite.

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