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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


x R y => x == y

I.e. different elements are not related.
References in periodicals archive ?
where the skew symmetric matrix Q is defined by Q = ([Q.
2] Ann Lee: Secondary symmetric, secondary skew symmetric, secondary orthogonal matrices; Period Math.
For each example, we took care that H was exactly symmetric and N exactly skew symmetric.
We discuss the numerical solution of eigenvalue problems for matrix polynomials, where the coefficient matrices are alternating symmetric and skew symmetric or Hamiltonian and skew Hamiltonian.
in which one matrix is symmetric and the other is skew symmetric.
i] as an alternating pencil or alternating matrix polynomial, since the coefficient matrices alternate between symmetric and skew symmetric.
18) with one coefficient matrix symmetric and the other skew symmetric.
The fact that one of A and B is symmetric and the other is skew symmetric forces the {[lambda], -[lambda]} pairing of the eigenvalues.