Editing Graded vector space (section)

==General gradation==
The subspaces of a graded vector space need not be indexed by the set of natural numbers, and may be indexed by the elements of any set ''I''.  An ''I''-graded vector space ''V'' is a vector space together with a decomposition into a direct sum of subspaces indexed by elements ''i'' of the set ''I'':
: <math>V = \bigoplus_{i \in I} V_i.</math>

Therefore, an <math>\mathbb{N}</math>-graded vector space, as defined above, is just an ''I''-graded vector space where the set ''I'' is <math>\mathbb{N}</math> (the set of [[natural number]]s).

The case where ''I'' is the [[ring (mathematics)|ring]] <math>\mathbb{Z}/2\mathbb{Z}</math> (the elements 0 and 1) is particularly important in [[physics]]. A <math>(\mathbb{Z}/2\mathbb{Z})</math>-graded vector space is also known as a [[supervector space]].