skew-symmetric
|skew-sym-met-ric|
/ˌskjuː sɪˈmɛtrɪk/
opposite of symmetric (transpose = negative)
Etymology
'skew-symmetric' is a modern compound formed from 'skew' + 'symmetric'. 'symmetric' originates from Greek, specifically the word 'summetrikos'/'symmetrikós', where 'syn-' meant 'together' and 'metron' meant 'measure'.
'symmetric' passed into English via Latin and French (e.g. Latin 'symmetricus', Old French forms) and became the modern English 'symmetric'. 'skew' entered English earlier (Middle English) meaning 'slanting' or 'oblique', and the compound 'skew-symmetric' arose in 19th–20th century mathematical usage to describe the 'slanted/negated' form of symmetry.
Initially, components meant 'skew' = 'slant/oblique' and 'symmetric' = 'measured together'; in mathematical usage they combined to denote a relation opposite to ordinary symmetry (transpose equals negative) and retained that technical meaning.
Meanings by Part of Speech
Adjective 1
(mathematics) Describing a square matrix A for which the transpose equals its negative, i.e. A^T = -A; also called antisymmetric.
A skew-symmetric matrix satisfies A^T = -A; consequently, all diagonal entries are zero.
Synonyms
Antonyms
Last updated: 2025/11/22 13:42