CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field . [ 1 ] [ a ] For every vector space there exists a basis, [ b ] and all bases of a vector space have equal cardinality; [ c ] as a result, the dimension of a vector space is uniquely defined. We say V is finite-dimensional if the dimension of V is finite . The dimension of the vector space V over the field F can be written as dim F ( V ) or as [V : F], read "dimension of V over F ". When F can be inferred from context, dim( V ) is typically written. 1 Examples 2 Facts 3 Generalizations 3.1 Trace 4 See also 5 Notes 6 References 7 External links Examples [ edit ] The vector space R 3 has as a basis , and therefore we have dim R ( R 3...