adjective
- not commutative; (of an operation) not yielding the same result regardless of the order of the operands
Usage: mathematics; formal
Examples
- Matrix multiplication is noncommutative because AB does not always equal BA.
- In noncommutative algebra, the order of operations matters significantly.
- Subtraction is a noncommutative operation: 5 − 3 ≠ 3 − 5.
- Physicists study noncommutative geometry to understand quantum mechanics.
- The noncommutative property of division means 10 ÷ 2 ≠ 2 ÷ 10.