Eigenvalue and Generalized Eigenvalue Problems: Tutorial

• URL: http://arxiv.org/abs/1903.11240v3
• Date: Sat, 20 May 2023 11:09:17 GMT
• Title: Eigenvalue and Generalized Eigenvalue Problems: Tutorial
• Authors: Benyamin Ghojogh, Fakhri Karray, Mark Crowley
• Abstract summary: This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem.
• Score: 12.323996999894002
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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