antisymmetrical
|an-ti-sym-met-ri-cal|
🇺🇸
/ˌæn.ti.sɪˈmɛ.trɪ.kəl/
🇬🇧
/ˌæn.tɪ.sɪˈmɛ.trɪ.k(ə)l/
not symmetric / against symmetry
Etymology
'antisymmetrical' originates from modern English formation combining the Greek prefix 'anti-' (from Greek 'ἀντί') meaning 'against' and 'symmetrical' (from Greek 'συμμετρία' via Latin/French) meaning 'measure together/commensurateness'.
'antisymmetrical' developed by prefixing 'anti-' to the adjective 'symmetrical' (itself from Old French 'symétrie' and Latin/Greek 'symmetria'), and was established in technical contexts (19th–20th c.) especially in mathematics and physics.
Initially used simply to mean 'not symmetrical', the term later acquired specialized meanings in mathematics (relation-theory 'antisymmetric') and in linear algebra/physics (synonymous with 'skew-symmetric' for matrices/tensors).
Meanings by Part of Speech
Adjective 1
not symmetric; lacking symmetry or not arranged in a balanced, mirror-like way.
The sculpture's design is intentionally antisymmetrical to create a sense of tension.
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Adjective 2
in order theory/relations: (of a binary relation R) if aRb and bRa then a = b; i.e., the relation does not allow distinct elements to relate mutually.
The relation ≤ on real numbers is antisymmetrical: if a ≤ b and b ≤ a, then a = b.
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Adjective 3
in linear algebra/tensor analysis: skew-symmetric (i.e., a matrix or tensor equal to the negative of its transpose, A^T = −A).
The matrix of that bilinear form is antisymmetrical, so its transpose equals its negative.
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Last updated: 2025/09/10 03:22