Antisymmetric
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English
Etymology
From Template:Prefix.
Adjective
- Template:Lb 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.
- 1987, David C. Buchthal, Douglas E. Cameron, Modern Abstract Algebra, Prindle, Weber & Schmidt, page 479,
- The standard example for an antisymmetric relation is the relation less than or equal to on the real number system.
- Template:Quote-book
- 1987, David C. Buchthal, Douglas E. Cameron, Modern Abstract Algebra, Prindle, Weber & Schmidt, page 479,
- Template:Lb Whose sign changes on the application of a matrix transpose or some generalisation thereof:
- Template:Lb Whose transpose equals its negative (i.e., MT = −M);
- Template:Lb That changes sign when any two indices are interchanged (e.g., Tijk = -Tjik);
- Template:Lb For which B(w,v) = -B(v,w).
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