# Singular Value Decomposition (SVD)

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Lesson Summary:

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.

Lesson Description:

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.
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