MIT 18.102 Introduction to Functional Analysis, Spring 2021 - Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator

MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=-sfaHVFWBU8&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=22 We prove the Fredholm Alternative, the Maximum Principle and the Spectral Theorem for self-adjoint compact operators. The final result is analogous to the statement that every Hermitian matrix is diagonalizable. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.