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_^T_A.
Av = \(\sigma\)u gives orthonormal eigenvectors u of _AA_^T.
\(\sigma^2 =\) eigenvalue of A_^T_A = 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