High Quality Content by WIKIPEDIA articles! 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. This description depends on two fundamental facts: for every vector space there exists a basis (if one assumes the axiom of choice), and all bases of a vector space have equal cardinality (see dimension theorem for vector spaces); as a result the dimension of a vector space is uniquely defined. The dimension of the vector space V over the field F can be written as dimF(V) or as , read "dimension of V over F". When F can be inferred from context, often just dim(V) is written.