Is Laplacian a Vector?

The Laplacian is a scalar operator. If it is applied to a scalar field, it generates a scalar field.

Is Laplacian operator a vector?

Vector Laplacian

, is a differential operator defined over a vector field. The vector Laplacian is similar to the scalar Laplacian; whereas the scalar Laplacian applies to a scalar field and returns a scalar quantity, the vector Laplacian applies to a vector field, returning a vector quantity.

What is the Laplacian of a scalar field?

With one dimension, the Laplacian of a scalar field U(x) at a point M(x) is equal to the second derivative of the scalar field U(x) with respect to the variable x. ... It represents the infinitesimal variation of U(x) relative to an infinitesimal change in x at this point.