A Gentle Introduction to the Jacobian
In the literature, the term Jacobian is often interchangeably used to refer to both the Jacobian matrix or its determinant.
Both the matrix and the determinant have useful and important applications: in machine learning, the Jacobian matrix aggregates the partial derivatives that are necessary for backpropagation; the determinant is useful in the process of changing between variables.
In this tutorial, you will review a gentle introduction to the Jacobian.
After completing this tutorial, you will know:
- The Jacobian matrix collects all first-order partial derivatives of a multivariate function that can be used for backpropagation.
- The Jacobian determinant is useful in changing between variables, where it acts as a scaling factor between one coordinate space and