Vector operator - Alchetron, The Free Social Encyclopedia

A vector operator is a differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and curl:

grad ≡ ∇ div ⁡ ≡ ∇ ⋅ curl ≡ ∇ ×

The Laplacian is

∇ 2 ≡ div ⁡ grad ≡ ∇ ⋅ ∇

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.

∇ f

yields the gradient of f, but

f ∇

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.

References

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