Vector operator

A vector operator is a type of differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and curl::$operatorname\{grad\}\; equiv\; abla$:$operatorname\{div\}\; equiv\; abla\; cdot$:$operatorname\{curl\}\; equiv\; abla\; imes$

The Laplacian is:$abla^2\; equiv\; operatorname\{div\}\; operatorname\{grad\}\; equiv\; abla\; cdot\; abla$

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.:$abla\; f$yields the gradient of "f", but:$f\; abla$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.

ee also

*del
* D'Alembertian operator

Further reading

* H. M. Schey (1996) "Div, Grad, Curl, and All That: An Informal Text on Vector Calculus", ISBN 0-393-96997-5.