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:

The Laplacian is

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.

yields the gradient of f, but

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.

Further Reading

• div, grad, curl, and all that (an informal text on vector calculus), by h. m. schey

See also: del, D'Alembertian operator.