Super vector space

In mathematics, a super vector space is a ${\displaystyle \mathbb {Z} _{2}}$-graded vector space, that is, a vector space over a field ${\displaystyle \mathbb {K} }$ with a given decomposition of subspaces of grade ${\displaystyle 0}$ and grade ${\displaystyle 1}$. The study of super vector spaces and their generalizations is sometimes called super linear algebra. These objects find their principal application in theoretical physics where they are used to describe the various algebraic aspects of supersymmetry.

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