Singular Value Decomposition (SVD)
In this lecture on Singular Value Decomposition, the goal is to find an orthogonal basis in the row space that gets knocked over into an orthogonal basis in the column space. SVD is the factorization of a matrix into orthogonal and diagonal matrices, and it's applicable to any matrix whatsoever. By computing A transpose A and finding its eigenvectors, we can determine the V's, while the U's are obtained by multiplying A by A transpose and finding its eigenvectors. The singular values are the square roots of the eigenvalues, and once we have these, we can express the original matrix as U times the diagonal matrix of the singular values times V transpose.
Singular Value Decomposition (SVD) -- Lecture 29. A very important and critical Linear Algebra topic explained in depth.
Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- SVD Java Applet - Singular Value Decomposition Java applet to play around with that is used in the demo lecture.
- SVD Mini-Lecture - This is a mini-lecture demo lesson on Singular Value Decomposition.
- What is SVD?
- What is Singular Value Decomposition?
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Staff Review
This video does a very good job of explaining a topic that has become incredibly important to Linear Algebra, and brings a lot of what Linear Algebra is together. A must-see if you are looking for an explanation of Singular Value Decomposition (SVD).
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