Matrix Action 
Aligners and Hangers 
Matrix Subspaces  
Linear Systems, Pseudo-Inverse 
Condition Number 
Matrix Norm 
Rank One 
Data Compression 
Noise Filtering 
Todd Will
UW-La Crosse

Introduction to the Singular Value Decomposition

Todd Will
UW-La Crosse
partially supported by an ACS-Mellon Technology Grant

The Singular Value Decomposition (SVD) is a topic rarely reached in undergraduate linear algebra courses and often skipped over in graduate courses. 

Consequently relatively few mathematicians are familiar with what M.I.T. Professor Gilbert Strang calls "absolutely a high point of linear algebra." 

These pages are a brief introduction to SVD suitable for inclusion in a standard sophomore level linear algebra course. 

The lessons on coordinates, projections, matrix subspaces, and linear systems are standard linear algebra topics presented via the SVD.   The later lessons give example applications of SVD. 

Much of the terminology and many of the ideas presented in these pages come from the text Matrices, Geometry & Mathematica, by Bill Davis and Jerry Uhl. 

Please give feedback or request answer keys to the exercises via email by contacting


© 1999 Todd Will
Last Modified: November 03, 2003
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