Finitely Generated Vector Space

up:: 021a MOC Linear Algebra

A Vector Space $(V,+,\cdot )$ is said to be finitely generated if it has a finite Spanning Set $S\subseteq V$.

Namely, all elements in $V$ can be generated by a finite Linear Combination of vectors in $S$, with $S$ 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

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References

• Um Curso de Álgebra Linear, Flávio Ulhoa Coelho & Mary Lilian Lourenço. Editora EDUSP.