Commute, commutation or commutative may refer to: *

Commuting Commuting is periodically recurring travel between a place of residence and place of work or study, where the traveler, referred to as a commuter, leaves the boundary of their home community. By extension, it can sometimes be any regular o ...

, the process of travelling between a place of residence and a place of work

Mathematics

Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a p ...

, a property of a mathematical operation whose result is insensitive to the order of its arguments **

Equivariant map In mathematics, equivariance is a form of symmetry for function (mathematics), functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are Group action ( ...

, a function whose composition with another function has the commutative property **

Commutative diagram 350px, The commutative diagram used in the proof of the five lemma In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the s ...

, a graphical description of commuting compositions of arrows in a mathematical category **

Commutative semigroup In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists o ...

commutative monoid In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being . Monoids are semigroups with identity ...

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commu ...

, and

commutative ring In mathematics, a commutative ring is a Ring (mathematics), ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring prope ...

, algebraic structures with the commutative property **

Commuting matrices In linear algebra, two matrices A and B are said to commute if AB=BA, or equivalently if their commutator ,B AB-BA is zero. Matrices A that commute with matrix B are called the commutant of matrix B (and vice versa). A set of matrices A_1, \ldot ...

, sets of matrices whose products do not depend on the order of multiplication **

Commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...

, a measure of the failure of two elements to be commutative in a group or ring *

Commutation matrix In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K(''m'',''n'') is the ...

, a permutation matrix which is used for transforming the vectorized form of another matrix into the vectorized form of its transpose

Science and technology

Commutator (electric) A commutator is a rotary switch, electrical switch in certain types of electric motors and electrical generators that periodically reverses the Current (electricity), current direction between the rotor and the external circuit. It consists of a ...

, a rotary switch on the shaft of an electric motor or generator * Commutation (neurophysiology), how certain neural circuits in the brain exhibit noncommutativity *

Commutation (telemetry) In telemetry, commutation is a process whereby multiple data streams ("measurands"), possibly with differing data rates, are combined into a single frame-based stream for transmission, before being separated again (decommutated) upon reception ...

, a form of time-division multiplexing * Commutation, a synonym for

packet switching In telecommunications, packet switching is a method of grouping Data (computing), data into short messages in fixed format, i.e. ''network packet, packets,'' that are transmitted over a digital Telecommunications network, network. Packets consi ...

in computer networking and telecommunications

Other uses

Commutation (law) In law, a commutation is the substitution of a lesser penalty for that given after a conviction for a crime. The penalty can be lessened in severity, in duration, or both. Unlike most pardons by government and overturning by the court (a full ove ...

(of sentence), a reduction in severity of punishment *

Commutation Commute, commutation or commutative may refer to: * Commuting, the process of travelling between a place of residence and a place of work Mathematics * Commutative property, a property of a mathematical operation whose result is insensitive to th ...

(finance) (law) to lessen periodic dues (usually rents, fares or tithes) by paying a lump sum * Commutation (finance) under a cash option, encashment. The act of a

pension A pension (; ) is a fund into which amounts are paid regularly during an individual's working career, and from which periodic payments are made to support the person's retirement from work. A pension may be either a " defined benefit plan", wh ...

member/annuitant who gives up part or all in exchange for a lump sum payment. {{disambiguation