up:: 021a MOC Linear Algebra A Vector Space is said to be finitely generated if it has a finite Spanning Set . Namely, all elements in can be generated by a finite Linear Combination of vectors in , with itself being finite. Properties Every linearly independent set of a finitely generated vector space has at most the same number of vectors as its spanning set References Um Curso de Álgebra Linear, Flávio Ulhoa Coelho & Mary Lilian Lourenço. Editora EDUSP.