{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/eigenvalue-and-generalized-eigenvalue","title":"Eigenvalue and Generalized Eigenvalue Problems: Tutorial","arxiv_id":"1903.11240","date":"2019-03-25","proceeding":null,"authors":["Benyamin Ghojogh","Fakhri Karray","Mark Crowley"],"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.","url_abs":"https://arxiv.org/abs/1903.11240v3","url_pdf":"https://arxiv.org/pdf/1903.11240v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"eigenvalue-and-generalized-eigenvalue","repo_url":"https://github.com/bghojogh/Generalized-Eigenvalue-Problem","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"matrix-factorization-decomposition","task_name":"Matrix Factorization / Decomposition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1903.11240","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}