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Derivation

If we have an associative algebra A over a field k, then, a linear map, D:A→A is called a derivation if it satisfies Leibniz' law:

D(ab)=(Da)b+a(Db)

Examples of derivations are partial derivatives, Lie derivatives and the commutator with respect to an element of the algebra. Actually, 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.

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Derivation".