AI engineering glossary · Calculus optimisation
What is hessian matrix?
Hessian matrix (also called Hessian): The square matrix of all second-order partial derivatives of a scalar function. It describes curvature: how the slope itself changes in every direction. Its eigenvalues reveal whether a stationary point is a minimum, maximum or saddle, and it drives Newton-type optimisers.
Hessian matrix: an example
For f(x, y) = x^2 + 3y^2, the Hessian is [[2, 0], [0, 6]], so the surface curves three times more sharply along y than along x.
Related terms
More Calculus optimisation terms
- Integral
- Jacobian matrix
- Jacobian-vector product
- KKT conditions
- L-BFGS
- L-smoothness
- Lagrange multiplier
- Lagrangian
Where you learn it
Hessian 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.