non-commutativeadj.
/ˌnɒnkəˈmjuːtətɪv/, /ˌnɒnˈkɒmjᵿtətɪv/, /ˌnɒnˈkɒmjᵿteɪtɪv/, U.S. /ˌnɑnˈkɑmjəˌteɪdɪv/, /ˌnɑnkəˈmjudədɪv/ Mathematics.
Not obeying the commutative law; (of a binary operation) giving a result that depends on the order of the quantities involved.
ΚΠ
1861 Proc. Royal Soc. 11 85 It became then necessary to invent an algebra of non-commutative symbols.
1880 Analyst 7 186 The non-commutative principle of quaternion (or vector) multiplication.
1950 P. B. Kershner & L. R. Wilcox Anat. Math. vii. 86 The theory of noncommutative groups has also proved to be useful..in modern physics.
1988 New Scientist 11 Aug. 54/1 Because gravity controls the geometry of space-time, the geometry itself should be non-commutative.
This entry has been updated (OED Third Edition, December 2003; most recently modified version published online March 2022).
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adj.1861