Orthogonal Diagonalization Explained - Linear Algebra

Explore orthogonal diagonalization in this 17-minute linear algebra video. Delve into orthogonal similarity and the Fundamental Theorem of Symmetric Matrices, establishing the connection between symmetric matrices and orthogonal diagonalizability. Learn how to orthogonally diagonalize a matrix step-by-step using eigenvectors and the Gram-Schmidt process. Follow along with a detailed example of orthogonally diagonalizing a 3x3 matrix. Gain insights into the symmetry of orthogonal similarity and understand why eigenvectors from distinct eigenspaces are orthogonal. Perfect for students and enthusiasts looking to deepen their understanding of linear algebra concepts.

Intro
Orthogonal Similarity
Symmetry of Orthogonal Similarity
Orthogonally Diagonalizable
Eigenvectors from Distinct Eigenspaces are Orthogonal
Fundamental Theorem of Symmetric Matrices
Step by Step Orthogonal Diagonalization
Orthogonal Diagonalization of a 3x3 Matrix
Conclusion