Georg Hamel in the context of Hamel dimension

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. We say ${\displaystyle V}$ is finite-dimensional if the dimension of ${\displaystyle V}$ is finite, and infinite-dimensional if its dimension is infinite.