18.06SC | Fall 2011 | Undergraduate

Linear Algebra

Unit III: Positive Definite Matrices and Applications

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 4th edition or Section 7.1 and 7.2 in the 5th edition.

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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Course Info

As Taught In
Fall 2011
Learning Resource Types
Lecture Videos
Exams with Solutions
Lecture Notes
Recitation Videos
Problem Sets with Solutions
Course Introduction
Instructor Insights