Editing Graded vector space (section)

{{Short description|Algebraic structure decomposed into a direct sum}}
{{Use American English|date = February 2019}}
In [[mathematics]], a '''graded vector space''' is a [[vector space]] that has the extra structure of a ''grading'' or ''gradation'', which is a decomposition of the vector space into a [[direct sum of vector spaces|direct sum]] of [[linear subspace|vector subspaces]], generally indexed by the [[integer]]s.

For "pure" vector spaces, the concept has been introduced in [[homological algebra]], and it is widely used for [[graded algebra]]s, which are graded vector spaces with additional structures.