up:: Finitely Generated Vector Space Let be a finitely generated vector space, and . Then is said to be a (Hamel) basis if Spans (by finite Linear Combinations) is Linearly Independent (ensures that all vectors in have a unique linear combination from ) Properties Every finitely generated vector space has a Hamel basis All Hamel bases have the same number of elements (in a finitely generated vector space) Sets larger than a finitely generated space’s bases are linearly dependent