  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. Finally, we introduce the solutions to both eigenvalue and
generalized eigenvalue problems.
