Super Vector Space
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a super vector space is another name for a Z2-graded vector space, that is, a vector space over a field K with a given decomposition V=V_0oplus V_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 described the various algebraic aspects of supersymmetry. Vectors which are elements of either V0 or V1 are said…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a super vector space is another name for a Z2-graded vector space, that is, a vector space over a field K with a given decomposition V=V_0oplus V_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 described the various algebraic aspects of supersymmetry. Vectors which are elements of either V0 or V1 are said to be homogeneous. The parity of a nonzero homogeneous element, denoted by x , is 0 or 1 according to whether it is in V0 or V1. x = begin{cases}0 & xin V_01 & xin V_1end{cases} Vectors of parity 0 are called even and those of parity 1 are called odd. Definitions for super vector spaces are often given only in terms of homogeneous elements and then extended to nonhomogeneous elements by linearity. If V is finite-dimensional and the dimensions of V0 and V1 are p and q respectively, then V is said to have dimension p q.