Background for antisymmetric

antisymmetric

/ˌæntiːsɪˈmɛtrɪk/ /ˌæntaɪsɪˈmɛtrɪk/

Illustration antisymmetric - Image 1

adjective

(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.

Examples :

"The "is older than or the same age as" relationship is antisymmetric because if person A is older than or the same age as person B, and person B is older than or the same age as person A, then person A and person B must be the same age. "

math logic system

Illustration antisymmetric - Image 1

adjective

(of certain mathematical objects) Whose sign changes on the application of a matrix transpose or some generalisation thereof:

Examples :

"The seating arrangement at the debate club was antisymmetric: if Maya sits to the left of David, then David must sit to the left of Maya in the next round. "