Introduction Matrix Action Perpframes, Aligners and Hangers Stretchers Coordinates Projections SVD Matrix Subspaces Linear Systems, PseudoInverse Condition Number Matrix Norm Rank One Data Compression Noise Filtering
Todd Will

Introduction to the Singular Value Decomposition 

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 will.todd@uwlax.edu
