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[[Category:MA271Fall2020Walther]] | [[Category:MA271Fall2020Walther]] | ||

+ | ==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: | ||

+ | |||

+ | <math>\Delta F = \nabla^2 F = \nabla (\nabla \cdot F) - \nabla \times (\nabla \times F) \\</math> | ||

+ | |||

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

+ | |||

+ | <math> | ||

+ | \Delta F = | ||

+ | \left[\begin{array} {1} | ||

[[Walther_MA271_Fall2020_topic9|Back to main page]] | [[Walther_MA271_Fall2020_topic9|Back to main page]] |

## Revision as of 00:03, 7 December 2020

## 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]] $