antisymmetric
|an-ti-sym-met-ric|
/ˌæn.ti.sɪˈmɛ.trɪk/
opposite of symmetric / lacking mutual symmetry
Etymology
'antisymmetric' originates from the Greek prefix 'anti-' (from Greek 'antí') meaning 'against, opposite' combined with 'symmetric' (from Greek roots meaning 'measured together').
'antisymmetric' was formed in Modern English by prefixing 'anti-' to 'symmetric'; 'symmetric' itself entered English via Latin and Old French from Greek 'summetria'/'summetros' (literally 'measured together').
Initially a general formation meaning 'opposed to or negating symmetry'; over time it acquired specialized technical meanings in mathematics and physics (for relations, matrices, tensors, etc.).
Meanings by Part of Speech
Adjective 1
in mathematics, describing a binary relation R on a set such that for any a and b, if aRb and bRa then a = b (i.e. no two distinct elements are mutually related).
The relation ≤ on real numbers is antisymmetric: if a ≤ b and b ≤ a then a = b.
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Adjective 2
describing a matrix or tensor that equals the negative of its transpose (also called skew-symmetric): A^T = −A (hence diagonal entries are zero over fields of characteristic ≠ 2).
In linear algebra, an antisymmetric matrix A satisfies A^T = -A.
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Last updated: 2025/09/10 03:08