Is the Laplacian a Vector or Scalar?

[iVenky]

Here's the link that I read for Laplacian-

http://hyperphysics.phy-astr.gsu.edu/hbase/lapl.html

It looks as if the laplacian is scalar but the point is we know that

∇x∇xA= ∇(∇.A) - ∇²A

This means that laplacian should be vector in nature which contradicts what was given in the link mentioned above.

Would be happy if you could clear my doubt as I am new to EMF.

Thanks a lot.

 

[Muphrid]

The Laplacian of a scalar field is a scalar field, and the Laplacian of a vector field is a vector field.

Edit: because it preserves scalars vs. vectors, it is common to refer to it as a scalar operator.