AI engineering glossary · Calculus optimisation
What is jacobian matrix?
Jacobian matrix (also called Jacobian): The matrix of all first-order partial derivatives of a vector-valued function: entry (i, j) is the derivative of output i with respect to input j. It describes the best linear approximation of the function near a point and generalises the gradient.
Jacobian matrix: an example
For f(x, y) = (x*y, x + y), the Jacobian is [[y, x], [1, 1]]; at (2, 3) it is [[3, 2], [1, 1]].
Related terms
More Calculus optimisation terms
- Jacobian-vector product
- KKT conditions
- L-BFGS
- L-smoothness
- Lagrange multiplier
- Lagrangian
- Learning rate
- Learning rate schedule
Where you learn it
Jacobian matrix is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.