Jacobian

The Jacobian is a mathematical tool used to understand how small changes in one set of variables affect another set, especially when transforming coordinates. Imagine mapping points from one coordinate system to another—like converting between geographic and Cartesian coordinates. The Jacobian provides a matrix that captures how distances and volumes scale during this transformation. It helps ensure that calculations, such as measuring areas or volumes, remain accurate when changing perspectives, by accounting for the local stretching or squeezing of space happening during the transformation.