Hessian

The Hessian is a mathematical concept used to understand how a function changes, especially in multiple dimensions. It is a matrix that contains second derivatives, which measure the curvature or how the slope of the function is changing at a point. Think of it as a tool that helps determine whether a point is a peak, a valley, or a saddle in a landscape. In optimization, the Hessian helps identify the nature of solutions and how to move toward the best value efficiently. It provides detailed insight into the function's local shape and behavior.