- #1

WWGD

Science Advisor

Gold Member

2019 Award

- 5,174

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## Main Question or Discussion Point

Hi,

Is there a way of representing the Laplacian ( Say for 2 variables, to start simple) ##\partial^2(f):= f_{xx}+f_{yy} ## as a "square of Jacobians" ( More precisely, as ##JJ^T ; J^T ## is the transpose of J, for dimension reasons)? I am ultimately trying to use this to show that the Laplacian is rotationally-invariant, using a rotation matrix and manipulating the product.

Is there a way of representing the Laplacian ( Say for 2 variables, to start simple) ##\partial^2(f):= f_{xx}+f_{yy} ## as a "square of Jacobians" ( More precisely, as ##JJ^T ; J^T ## is the transpose of J, for dimension reasons)? I am ultimately trying to use this to show that the Laplacian is rotationally-invariant, using a rotation matrix and manipulating the product.