Jacobian Matrix Calculation
Matrix Algebra DS practice problem on Onlearn.
Difficulty: medium.
Topics: Jacobian Matrix Calculation, Partial Derivatives, Chain Rule, Linear Approximation, Determinant Calculation, Computational Graph, Linear Algebra, Multivariable Calculus, Numerical Analysis, Optimization Theory, Differential Geometry, Matrix Calculus, Vector-Valued Functions, Automatic Differentiation, Coordinate Transformations, Sensitivity Analysis.
Implement a function to compute the Jacobian matrix of a vector valued function using numerical differentiation. The Jacobian matrix contains all first order partial derivatives of a function f: R^n R^m. Given a function f and a point x, approximate each partial derivative using finite differences and return the m x n Jacobian matrix.