Commute is what you do while you go from the place you live to the place you work. The longer it takes, the more annoying it is, especially if you are driving, unless you have a Laptop to play with if you are a geek. Non-geeks always hate their commutes.

Two elements of a group, a and b, commute if ab = ba. It is common in the study of linear algebra to consider whether two matrices commute. The group product in this case is just matrix multiplication.

In quantum mechanics, if two matrices that represent physical observables commute, then the observables can have simultaneous precise values. As an example, the operators representing energy and linear momentum of a free particle commute, so it is possible to know a free particle's energy and linear momentum simultaneously (neglecting relativistic effects, E = p2/2m). On the other hand, the operators representing linear momentum and position of a particle never commute, implying that a particle's position and velocity cannot be known simultaneously (see Heisenberg Uncertainty Principle).

The commutator of a and b, [a, b], is defined as ab - ba. If a and b commute, [a, b] = 0.

Com*mute" (?), v. t. [imp. & p. p. Commuted; p. pr. & vb. n. Commuting.] [L. commutare, -mutatum; com- + mutare to change. See Mutation.]

To exchange; to put or substitute something else in place of, as a smaller penalty, obligation, or payment, for a greater, or a single thing for an aggregate; hence; to lessen; to diminish; as, to commute a sentence of death to one of imprisonment for life; to commute tithes; to commute charges for fares.

The sounds water and fire, being once annexed to those two elements, it was certainly more natural to call beings participating of the first "watery", and the last "fiery", than to commute the terms, and call them by the reverse. J. Harris

The utmost that could be obtained was that her sentence should be commuted from burning to beheading. Macaulay.

Com*mute", v. i.

1.

To obtain or bargain for exemption or substitution; to effect a commutation.

He . . . thinks it unlawful to commute, and that he is bound to pay his vow in kind. Jer. Taylor.

2.

To pay, or arrange to pay, in gross instead of part by part; as, to commute for a year's travel over a route.