Dimension (Vector Space)

The dimension of a vector space V is the cardinality, that is the number of vectors, of a basis of V over its base field, and every basis of the same vector space has the same cardinality. This quantity is sometimes called the Hamel dimension or algebraic dimension, to distinguish it from other notions of dimension used elsewhere in mathematics. Dimension is one of the most basic invariants of a vector space, since it determines how many independent coordinates are needed to describe every vector in the space.