## Vector Laplacian

The Laplace operator is originally an operation where you input a scalar function and it returns a scalar function. However, there is an alternate version of the Laplace operator that can be performed on vector fields.

The vector Laplacian is defined as:

$ \Delta F = \nabla^2 F = \nabla (\nabla \cdot F) - \nabla \times (\nabla \times F) \\ $

where F is a vector field. In Cartesian coordinates, the vector Laplacian simplifies to the following:

$ \Delta F = \left[\begin{array} {1} [[Walther_MA271_Fall2020_topic9|Back to main page]] $