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antisymmetric
(redirected from Skew-symmetric)

   Also found in: Encyclopedia, Wikipedia 0.01 sec.
antisymmetric [ˌæntɪsɪˈmɛtrɪk]
adj
1. (Philosophy / Logic) Logic (of a relation) never holding between a pair of arguments x and y when it holds between y and x except when x = y, as ``…is no younger than…'' Compare nonsymmetric
2. (Mathematics) maths symmetric except for a change of sign Compare asymmetric, symmetric [1]


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Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Vector spaces, multilinear mappings, dual spaces, tensor product spaces, tensors, symmetric and skew-symmetric tensors, and exterior or Grassmann algebra are described in the initial chapters, with definitions and examples provided.
8) and then by using the skew-symmetric property of [phi], we get S([phi]Y,[phi]Z) = (n - 1)g([phi]Y,[phi]Z).
 
 
 
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