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JacobianMatrix (3.1.0) current version: 4.0.0 »

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Compute the Jacobian matrix of a vector function with respect to a list of variables

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["JacobianMatrix"][expr,{var₁,var₂,…}]

computes the Jacobian matrix of the expression expr with respect to the given variables.

Examples

Basic Examples (6)

Compute the Jacobian matrix of an expression:

In[1]:=

$ResourceFunction["JacobianMatrix"][{4 x^2 y, x - y^2}, {x, y, z}]$

Out[1]=

Compute the Jacobian matrix of an another expression:

In[2]:=

$ResourceFunction[ "JacobianMatrix"][{4 x^2 y, x - y^2}, {x, y}] // MatrixForm$

Out[2]=

Compute the Jacobian matrix of an another expression:

In[3]:=

Out[3]=

Compute the Jacobian matrix of an another expression:

In[4]:=

$ResourceFunction[ "JacobianMatrix"][{x y z, x^2 z}, {x, y, z}] // MatrixForm$

Out[4]=

Compute the Jacobian matrix of an another expression:

In[5]:=

$ResourceFunction[ "JacobianMatrix"][{r p Sin[t], r p Cos[t], r^2/p}, {r, p, t}] // MatrixForm$

Out[5]=

Compute the Jacobian matrix of an another expression:

In[6]:=

Out[6]=

Properties and Relations (3)

Compute the Jacobian matrix of an expression:

In[7]:=

$ResourceFunction[ "JacobianMatrix"][{x^3 - 2 x y - y^6, x - y^2}, {x, y}]$

Out[7]=

Take the determinant of this result:

In[8]:=

Out[8]=

Compare this to the result obtained using of ResourceFunction["JacobianDeterminant"]:

In[9]:=

$ResourceFunction["JacobianDeterminant"][{x^3 - 2 x y - y^6, x - y^2}, {x, y}]$

Out[9]=

Publisher

Wolfram|Alpha Math Team

Related Links

Version History

4.0.0 – 23 March 2023
3.1.0 – 12 May 2021
3.0.0 – 24 January 2020
2.0.0 – 06 September 2019
1.0.0 – 05 August 2019

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License Information

This work is licensed under a Creative Commons Attribution 4.0 International License