The Hessian Matrix
Calculus & Optimization DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Second-Order Derivatives in Optimization, Second-order partial derivatives, Symmetry of the Hessian (Schwarz's theorem), Finite difference approximation, Local extrema identification, Positive Definiteness, Multivariable Calculus, Numerical Analysis, Optimization Theory, Linear Algebra, Automatic Differentiation, Partial Derivatives, Gradient Vectors, Taylor Series Expansion, Curvature Analysis, Quadratic Forms.
Implement a function that computes the Hessian matrix for a given scalar function f(x, y). The Hessian is a square matrix of second order partial derivatives: H ij = d^2f / (dx i dx j). Assume the function is provided as a Python callable taking a list or array of variables.