🟦 Matrix equals negative transpose 🔄 Changes sign when swapped ↔️ Only equal if reversed

antisymmetric

1 9.0

A relation where if one thing relates to another, the reverse only happens when they are the same

adjective
/ˌæntiˈsɪmɛtrɪk/

Specialized

: antisimétrico

For a set to have an antisymmetric ordering, whenever two elements are related in both directions, they must be the same.

Examples

So, but for now, let's just call partial orders those that are reflexive, antisymmetric and transitive.
Let's see, Antisymmetric with respect to these two, yes.
A relation is antisymmetric if aRb and bRa imply a = b.
In mathematics, a binary relation is antisymmetric when it holds true that xRy and yRx lead to x equaling y.

Surface Forms

antisymmetric positive

Morphology

antisymmetric = symmetric (semi-transparent) = anti + symmetr + ic

The prefix anti- and base symmetric give a clear clue, but the formal condition about equality being required for the reverse relation is a technical mathematical definition.

Etymology

Antisymmetric comes from the parts anti- 'against' and symmetric 'same on both sides'. So an antisymmetric relation does not allow two different things to be linked both ways — if a is related to b and b to a, then a and b must be the same.