Derivation
In
abstract algebra, a
derivation on an
associative algebra A over a
field k is a linear map D:A→A that satisfies
Leibniz' law:
- D(ab) = (Da)b + a(Db).
Examples of derivations are
partial derivatives, Lie derivatives, the
Pincherle derivative, and the
commutator with respect to an element of the algebra. All these examples are tightly related, with the concept of derivation as the major unifying theme.
Derivation may also be used as a synonym for proof, particularly for formulae.