Singular Value Decomposition (SVD) Tutorial: Applications, Examples, Exercises

This singular value decomposition tutorial assumes you have a good working knowledge of both matrix algebra and vector calculus. We start with a short history of the method, then move on to the basic definition, including a brief outline of numerical procedures. This is then followed by a more intuitive derivation meant to demonstrate the meaning of singular value decomposition and then to a pair of common applications. The final section works out a complete program that uses SVD in a machine-learning context. To help you become more familiar with the material, exercises are provided throughout.