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antisymmetric
(redirected from Skew-symmetric)

   Also found in: Dictionary/thesaurus, Wikipedia 0.01 sec.
(mathematics)antisymmetric - A relation R is antisymmetric if,

for all x and y, x R y and y R x => x == y.

I.e. no two different elements are mutually related.

Partial orders and total orders are antisymmetric. If R is also symmetric, i.e.

x R y => y R x

then

x R y => x == y

I.e. different elements are not related.


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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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