Eigenvalue and Generalized Eigenvalue Problems: Tutorial

Understand

This paper is a tutorial for eigenvalue and generalized eigenvalue problems.

• We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem.
• Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems.
• We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems.