Singular Value Decomposition

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Session Overview

Figure excerpted from 'Introduction to Linear Algebra' by G.S. Strang

If A is symmetric and positive definite, there is an orthogonal matrix Q for which A = QΛQT. Here Λ is the matrix of eigenvalues. Singular Value Decomposition lets us write any matrix A as a product UΣVT where U and V are orthogonal and Σ is a diagonal matrix whose non-zero entries are square roots of the eigenvalues of ATA. The columns of U and V give bases for the four fundamental subspaces.

Session Activities

Lecture Video and Summary

Suggested Reading

  • Read Section 6.7 in the textbook.

Problem Solving Video

Check Yourself

Problems and Solutions

Work the problems on your own and check your answers when you're done.


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