Jacobian

Author

Eric W. Weisstein
August 9, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/Jacobian.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Jacobian.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

JacobianMatrix[f_List?VectorQ,x_List]:=Outer[D,f,x]/;Equal@@(Dimensions/@{f,x})

JacobianDeterminant[f_List?VectorQ,x_List]:= Det[JacobianMatrix[f,x]]/;Equal@@(Dimensions/@{f,x})

Examples

xs=Subscript[x,#]&/@Range[3]

fns=Through[(Subscript[f,#]&/@Range[3])[Sequence@@xs]]

JacobianMatrix[fns,xs]//MatrixForm

JacobianDeterminant[fns,xs]//MatrixForm