antisymmetry
|an-ti-sym-me-try|
/ˌæntɪˈsɪmɪtri/
not symmetric; sign-change or ordering property on exchange
Etymology
'antisymmetry' originates from Greek elements 'anti-' and 'symmetria', where 'anti-' meant 'against' and 'symmetria' meant 'measured together'.
'antisymmetry' was formed in modern English by prefixing the Greek-derived prefix 'anti-' to the existing English word 'symmetry' (from Greek 'symmetria' via Latin), producing the compound 'antisymmetry'.
Initially reflecting the general idea of 'opposition to symmetry', it evolved into the technical sense used in mathematics and physics to denote either the sign-change property under exchange or the order-theoretic property described above.
Meanings by Part of Speech
Noun 1
a property of a binary relation R on a set: for all a and b, if aRb and bRa then a = b.
The relation ≤ on real numbers is antisymmetry; if a ≤ b and b ≤ a then a = b.
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Noun 2
the property of a function, tensor, or wavefunction that changes sign when two arguments (or indices, or particles) are exchanged (f(x,y) = -f(y,x)). Often called skew-symmetry in linear algebra.
The wavefunction of identical fermions exhibits antisymmetry under particle exchange.
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Last updated: 2025/09/10 02:54