antisymmetric

(redirected from Skew-symmetric)
Also found in: Dictionary.
Related to Skew-symmetric: Skew-symmetric matrix, Skew-symmetric bilinear form

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.
References in periodicals archive ?
Further, if A is a skew-symmetric matrix, then we write [A.
In this paper we will focus on complex matrix polynomials, where the coefficient matrices are complex symmetric or skew-symmetric, i.
3] is a skew-symmetric matrix associated to the unit vector [[?
In addition, by establishing iterative algorithm, the symmetric solution, skew-symmetric solution, Hermitian least-norm solution of matrix equation (1) have been derived in [10-12], respectively.
A curious byproduct of our formula (originally due to Jones [Jon]) is that it also counts the number of symmetric matrices in GL(n - 1, q) and the number of skew-symmetric matrices in GL(n, q).
A] refer to the scalar, the deviatoric, and the skew-symmetric parts, respectively.
Here, M and K are positive definite mass and stiffness matrices and G is the skew-symmetric gyroscopic matrix resulting from the Coriolis force.
The fact that U is isotropic is equivalent to the property that the matrix A is skew-symmetric.
If we want to obtain the energy balance by integration, we obtain that the variation of energy due to the term skew-symmetric is null.
We further mention the decay bounds for functions of banded skew-symmetric matrices given in [21, 56] which, however, were obtained using different techniques from ours.