Linear Algebra Lectures 2025 - Linear Algebra Lectures - Lecture 41B Proof of the Symmetric Matrix Theorem

This video contains a proof of the Symmetric Matrix Theorem, which states that a square matrix is orthogonally diagonalizable if and only if the matrix is symmetric. Other than some facts about complex numbers (which are explained in the video), this proof only relies on ideas from earlier in this course. Textbook: https://webspace.ship.edu/jehamb/ela/ Playlist: https://www.youtube.com/playlist?list=PLNr8B4XHL5kGwxiRYcUW3dCQGuA09d3xO If you are an instructor, contact me for more information about the over 300 online homework problems that I have created for the free MyOpenMath platform (https://www.myopenmath.com). If you are a student interested in learning more and working on practice problems, you can enroll in the Elementary Linear Algebra self-study course on MyOpenMath. Go to https://www.myopenmath.com, and click "Student Self Study" at the top of the page. Follow the instructions to create a student account and enroll in the course.