Langimage
English

skew-symmetry

|skew-sym-me-try|

C2

🇺🇸

/skjuː ˈsɪmətri/ or /skuː ˈsɪmətri/

🇬🇧

/skjuː ˈsɪmətri/

transpose equals negative

Etymology
Etymology Information

'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).

Historical Evolution

'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'.

Meaning Changes

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