In mathematics, particularly in the field of functional analysis and theoretical physics, a **super vector space** (or **Z_2-graded vector space**) is a generalization of the concept of a vector space. It incorporates the idea of a grading, often used to describe systems that have distinct symmetrical properties or to handle Fermionic fields in physics.
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A super vector space is a vector space graded by the two-element group. Degree-preserving maps and the usual graded tensor product form a monoidal category. Over a field of characteristic different from two, this category has two different symmetries: ordinary interchange of tensor factors and interchange multiplied by on homogeneous factors of degrees . The latter is the Koszul sign rule.