121. Hessian Matrix
121.1. Hessian Matrix
Square matrix of second-order partial derivatives
Describes the local curvature of a multivariable function
Input:
Output: Scalar
Diagonal entries:
Second derivative of with respect to a single variable twice
How the slope of changes as you move along the direction
Off-diagonal entries: where
How the slope in one direction changes when you move in a different direction
: How the rate of change of along changes as you move in the direction
Symmetric (Clairaut-Schwarz theorem):
Example
- Symbolic Hessian
- Evaluate at
Each entry is now a scalar, and the Hessian is numeric