Lecture 6: Singular Value Decomposition (SVD)

Description

Singular Value Decomposition (SVD) is the primary topic of this lecture. Professor Strang explains and illustrates how the SVD separates a matrix into rank one pieces, and that those pieces come in order of importance.

Summary

Columns of V are orthonormal eigenvectors of A^TA.
Av = \(\sigma\)u gives orthonormal eigenvectors u of AA^T.
\(\sigma^2 =\) eigenvalue of A^TA = eigenvalue of AA^T \( \neq\) 0
A = (rotation)(stretching)(rotation) \(U\Sigma\)V^T for every A

Related section in textbook: I.8

Instructor: Prof. Gilbert Strang