Jacobian Calculator
Calculate the Jacobian matrix and determinant of a vector-valued function.
Vector Function F(x, y, z)
Point of Evaluation
Jacobian Matrix Formula
J = [df1/dx df1/dy df1/dz]
[df2/dx df2/dy df2/dz]
[df3/dx df3/dy df3/dz]
Jacobian Determinant
0.000000
Not invertible (det = 0)
Jacobian Matrix
| 2.0000 | 1.0000 | 0.0000 |
| 2.0000 | 1.0000 | 0.0000 |
| 0.0000 | 1.0000 | 1.0000 |
detDeterminant
0.000000
trTrace
4.000000
Function Values at Point
f1(x,y,z)3.000000
f2(x,y,z)2.000000
f3(x,y,z)3.000000
About the Jacobian
Definition
The Jacobian matrix contains all first-order partial derivatives of a vector-valued function. Its determinant measures how the function locally scales volumes during transformation.
Applications
- Change of variables in integration
- Inverse function theorem
- Robotics and kinematics
- Coordinate system transformations