Dimension (vector space)

Common card · No. 387653

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. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension. For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. V {\displaystyle V} is said to be finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space V {\displaystyle V} over the field F {\displaystyle F} can be written as dim F ⁡ ( V )...

Read on Wikipedia · Image NerdBoy1392, CC BY-SA 3.0