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A '''vector operator''' is a [[differential operator]] used in [[vector calculus]]. Vector operators are defined in terms of [[del]], and include the [[gradient]], [[divergence]], and [[Curl (mathematics)|curl]]:
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:<math> \operatorname{grad} \equiv \nabla </math>
:<math> \operatorname{div} \ \equiv \nabla \cdot </math>
:<math> \operatorname{curl} \equiv \nabla \times </math>


The [[Laplacian]] is
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:<math> \nabla^2 \equiv \operatorname{div}\ \operatorname{grad} \equiv \nabla \cdot \nabla </math>
 
Vector operators must always come right before the [[scalar field]] or [[vector field]] on which they operate, in order to produce a result. E.g.
:<math> \nabla f </math>
yields the gradient of ''f'', but
:<math> f \nabla </math>
is just another vector operator, which is not operating on anything.
 
A vector operator can operate on another vector operator, to produce a compound vector operator, as seen above in the case of the Laplacian.
 
==See also==
* [[del]]
* [[D'Alembertian operator]]
* [http://modis.ispras.ru/wikipedia/pic/Vector_calculus.html Related articles on a diagram]
 
==Further reading==
* H. M. Schey (1996) ''Div, Grad, Curl, and All That: An Informal Text on Vector Calculus'', ISBN 0-393-96997-5.
 
[[Category:Vector calculus]]

Latest revision as of 15:24, 25 October 2014

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