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:

[itex] \operatorname{div} \ \equiv \nabla \cdot [itex]
[itex] \operatorname{curl} \equiv \nabla \times [itex]

The Laplacian is

[itex] \nabla^2 \equiv \operatorname{div}\ \operatorname{grad} \equiv \nabla \cdot \nabla [itex]

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.

[itex] \nabla f [itex]

yields the gradient of f, but

[itex] f \nabla [itex]

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

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