antisymmetric

Meanings

Adj

• 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.
• Whose sign changes on the application of a matrix transpose or some generalisation thereof:
• Whose transpose equals its negative (i.e., Mᵀ = −M);
• Whose sign changes on the application of a matrix transpose or some generalisation thereof:
• That changes sign when any two indices are interchanged (e.g., Tᵢⱼₖ = -Tⱼᵢₖ);
• Whose sign changes on the application of a matrix transpose or some generalisation thereof:
• For which B(w,v) = -B(v,w).

Synonyms

skew-symmetric

Related Words

anticommutative, antisymmetry, skew-symmetric, symmetric