information:filtering, stylistic:tone, structural:scholar_edition
Vector spaces

The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.

For the non- free case, this generalizes to the notion of the length of a module.