Derivatives, Gradients, Jacobians, and Hessians: A Deep Dive
2025-08-17
This article provides a clear explanation of derivatives, gradients, Jacobian matrices, and Hessian matrices, four fundamental concepts in calculus and their applications. Derivatives describe the rate of change of a function, gradients point in the direction of the greatest increase, Jacobian matrices describe the warping of space for multivariable functions, and Hessian matrices contain second-order derivatives, describing curvature. These concepts are crucial in optimization algorithms (like gradient descent) and computer graphics (e.g., anti-aliasing rendering), providing a deeper understanding of machine learning and graphics rendering.
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matrices