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noncommutative
This term is used exclusively within the specialized domain of mathematics, specifically in abstract algebra and linear algebra. It describes a system where the sequence of elements is critical, meaning that changing the order of operations produces a different outcome. This stands in direct opposition to commutative properties, where order is irrelevant, such as in basic addition or multiplication of real numbers.
In practical application, the term most frequently appears when discussing matrix multiplication or the behavior of certain groups and rings. It carries a neutral, technical connotation and is never used in casual conversation or non-mathematical contexts to describe general disorder or sequence.
Meanings
Examples
Matrix multiplication is a noncommutative operation.
Matrix multiplication is a noncommutative operation.
In quantum mechanics, the position and momentum operators are noncommutative.
Wait, is this ring noncommutative or commutative?
Wait, is this ring noncommutative or commutative?
The student struggled to understand why the algebra was noncommutative.
We are dealing with a noncommutative geometry here.
If the operation is noncommutative, the order of elements matters.
I wonder if there are any noncommutative groups in this set.
The professor explained the properties of noncommutative rings.