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.
 div, grad, curl, and all that (an informal text on vector calculus), by h. m. schey
See also: del,
D'Alembertian operator.