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Was (wer) ist antisymmetric - definition
WIKIMEDIA DISAMBIGUATION PAGE
Skew-symmetric; Anti-symmetric; Antisymmetric (disambiguation)
antisymmetric
<mathematics> 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.
(1995-04-18)
antisymmetric
¦ adjective Mathematics & Physics unaltered in magnitude but changed in sign by an arithmetical or symmetry operation.
Antisymmetric tensor
TENSOR EQUAL TO THE NEGATIVE OF ANY OF ITS TRANSPOSITIONS
Alternating tensor; Completely antisymmetric tensor; Anti-symmetric tensor; Skew-symmetric tensor; Totally antisymmetric tensor
In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged. section §7.
Wikipedia
Antisymmetric
Antisymmetric or skew-symmetric may refer to:
- Antisymmetry in linguistics
- Antisymmetric relation in mathematics
- Skew-symmetric graph
- Self-complementary graph
In mathematics, especially linear algebra, and in theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (e.g. matrix transposition) is performed. See:
- Skew-symmetric matrix (a matrix A for which AT = −A)
- Skew-symmetric bilinear form is a bilinear form B such that B(x, y) = −B(y, x) for all x and y.
- Antisymmetric tensor in matrices and index subsets.
- "antisymmetric function" – odd function
