komutativiteti

Komutativiteti, known in English as commutativity, is the property of a binary operation on a set S such that changing the order of the operands does not change the result. If a ∘ b = b ∘ a for all a, b in S, the operation ∘ is called commutative. When a set equipped with a binary operation has this property for its operation, the structure may be described as commutative; in algebra, abelian structures are those whose binary operation is commutative, for example abelian groups, rings, and algebras.

Common examples include addition and multiplication of real numbers, integers, and more generally any field: a + b = b + a and a · b = b · a. Set operations such as union and intersection are also commutative. Logical conjunction (AND) and bitwise XOR are other examples of commutative operations.

Not all operations are commutative. Matrix multiplication, for instance, is generally non-commutative since AB ≠ BA in general. Function composition is non-commutative in most cases, though sometimes specific pairs of functions commute. The concept can be extended to partial commutativity, where the property holds for a subset of pairs.

Etymology: the term derives from Latin com- “together” and mutare “to change,” reflecting the idea that the order of factors can be exchanged without affecting the outcome.