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Vector operator

Differential operator used in vector calculus From Wikipedia, the free encyclopedia

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A vector operator is a differential operator used in vector calculus.[1] Vector operators include:

Defined in terms of del:

The Laplacian operates on a scalar field, producing a scalar field:

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.

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