antisymmetric.
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.
Meaning & usage
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).
Where this word comes from
Etymology tree Proto-Indo-European *h₂ent- Proto-Indo-European *-s Proto-Indo-European *h₂énts Proto-Indo-European *-i Proto-Indo-European *h₂énti Ancient Greek ᾰ̓ντῐ́ (ăntĭ́) Ancient Greek ἀντι- (anti-)der. English anti- English symmetric English antisymmetric From anti- + symmetric.
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Definitions, grammatical labels, IPA, etymology and examples: Wiktionary contributors, extracted by Kaikki / Wiktextract. Adapted under CC BY-SA 4.0. Selected fields and authored examples are shown; third-party quotations and audio are omitted. See contributor history.
Last enriched 2026-09-10. Definitions are in English. Romanizations are shown when supplied by the source; syllable estimates are omitted for unsupported scripts.