Jacobian matrix

The Jacobian matrix is a mathematical tool that describes how a set of output values changes when the input values change. Imagine it as a map showing the rate of change for each output with respect to each input. It’s especially useful in fields like robotics and physics to understand how small changes in inputs, such as joint angles, affect outputs like position or velocity. Essentially, the Jacobian provides a precise way to analyze and control how a system responds to changes, helping in tasks like navigation, optimization, and simulation.