Advanced Linear Algebra - Lecture 34: The Singular Value Decomposition

We introduce and prove the principal singular value decomposition of a real or complex matrix. We also demonstrate how to calculate it, and illustrate with some examples. Textbook: http://www.njohnston.ca/publications/advanced-linear-and-matrix-algebra/ Blank course notes (lectures 34-37): http://www.njohnston.ca/ala_week9.pdf Annotated course notes (lectures 34-37): http://www.njohnston.ca/ala_week9_annotated.pdf Please leave a comment below if you have any questions, comments, or corrections. Timestamps: 00:00 - Introduction 00:42 - The SVD 08:19 - Computing singular values 13:39 - Computing a full SVD 23:34 - (Conjugate) transpose of SVD