Session Overview
If A is symmetric and positive definite, there is an orthogonal matrix Q for which A = QΛQ^{T} . Here Λ is the matrix of eigenvalues. Singular Value Decomposition lets us write any matrix A as a product UΣV^{T} where U and V are orthogonal and Σ is a diagonal matrix whose non-zero entries are square roots of the eigenvalues of A^{T}A. The columns of U and V give bases for the four fundamental subspaces. |
Session Activities
Lecture Video and Summary
- Watch the video lecture Lecture 29: Singular Value Decomposition
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)
Suggested Reading
- Read Section 6.7 in the 4^{th} edition or Section 7.1 and 7.2 in the 5^{th} edition.
Problem Solving Video
- Watch the recitation video on Problem Solving: Computing the Singular Value Decomposition
- Recitation video transcript (PDF)
Check Yourself
Problems and Solutions
Work the problems on your own and check your answers when you’re done.