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In mathematics, a super vector space is a Z2-graded vector space, that is, a vector space over a field ''K'' with a given decomposition : 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. ==Definitions== Vectors which are elements of either ''V''0 or ''V''1 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 ''V''0 or ''V''1. : 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 ''V''0 and ''V''1 are ''p'' and ''q'' respectively, then ''V'' is said to have ''dimension'' ''p''|''q''. The standard super coordinate space, denoted ''K''''p''|''q'', is the ordinary coordinate space ''K''''p''+''q'' where the even subspace is spanned by the first ''p'' coordinate basis vectors and the odd space is spanned by the last ''q''. A ''homogeneous subspace'' of a super vector space is a linear subspace that is spanned by homogeneous elements. Homogeneous subspaces are super vector spaces in their own right (with the obvious grading). For any super vector space ''V'', one can define the ''parity reversed space'' Π''V'' to be the super vector space with the even and odd subspaces interchanged. That is, : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「super vector space」の詳細全文を読む スポンサード リンク
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