Jacobian & Hessian Matrix

Jacobian matrix

• represents the rate of change of a vector-valued function with respect to its input variables
• contains the partial derivatives of each component of y with respect to each component of x
• provides information about the local linear transformations at a given point.

The Hessian matrix

• is derived from the Jacobian matrix
• characterizes the second-order partial derivatives of a scalar-valued function
• is used in optimization to analyze the curvature of the function's graph