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:
- <math> \operatorname{grad} \equiv \nabla </math>
- <math> \operatorname{div} \ \equiv \nabla \cdot </math>
- <math> \operatorname{curl} \equiv \nabla \times </math>
The Laplacian is
- <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
Further reading
- H. M. Schey (1996) Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, ISBN 0-393-96997-5.
