skew-symmetry
|skew-sym-me-try|
🇺🇸
/skjuː ˈsɪmətri/ or /skuː ˈsɪmətri/
🇬🇧
/skjuː ˈsɪmətri/
transpose equals negative
Etymology
'skew-symmetry' originates from modern English, composed of the word 'skew' and the word 'symmetry', where 'skew' meant 'crooked' or 'oblique' and 'symmetry' derives from Greek 'symmetria' meaning 'measured together' ('syn-' together + 'metron' measure).
'skew' developed in English from earlier senses of 'crooked, at an angle' (recorded in Middle English and Scots), while 'symmetry' came into English via Latin 'symmetria' from Greek 'symmetria'; the combined mathematical compound 'skew-symmetry' is a modern formation used in 19th–20th century mathematical literature to name the property, paralleling terms like 'skew-symmetric'.
Initially, 'skew' referred to being slanted or oblique and 'symmetry' to balanced proportion; over time the compound came to denote the specific algebraic property 'A^T = -A' in linear algebra rather than a general visual slant or balance.
Meanings by Part of Speech
Noun 1
in linear algebra, the property of a square matrix A such that A^T = -A (its transpose equals its negative); also called antisymmetry in some contexts.
Skew-symmetry of a matrix means A^T = -A; for example, the matrix [[0, 1], [-1, 0]] has skew-symmetry.
Synonyms
Antonyms
Last updated: 2025/11/22 13:20
