最終更新日：2024/07/29

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(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.

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antisymmetric

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antisymmetric

adj

The relation R is antisymmetric if for all a and b in the set A, if (a, b) ∈ R and (b, a) ∈ R, then a = b.

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(of a matrix) Whose transpose equals its negative (i.e., Mᵀ = −M);

The eigenvalues of an antisymmetric matrix are all purely imaginary numbers, and occur as conjugate pairs, +iw and -iw. As a corollary it follows that an antisymmetric matrix of odd order necessarily has one eigenvalue equal to zero; antisymmetric matrices of odd order are singular.

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