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A Constructive Approach to Singular Value Decomposition and Symmetric Schur Factorization

This is an article from The American Mathematical Monthly, Vol. 112, No. 4 (Apr., 2005), pp. 358-363.  The authors prove the existance of the singular value decomposition without reference to eigenvalues and eigenvectors, by instead developing a constructive proof.  They then show that a small modification of their argument can be used to prove the existance of the symmetric Schur factorization.  The article is clearly written and is quite interesting.  However, the level is such that most students in a typical linear algebra course would need considerable guidance to get through it.  It seems like it would be well suited for a more advanced undergraduate with a deeper mathematics background.

Identifier: 
http://www.jstor.org/stable/pdfplus/10.2307/30037473.pdf?acceptTC=true
Rating: 
Average: 4 (1 vote)
Creator(s): 
John Clifford, David James, Michael Lachance and Joan Remski
Cataloger: 
Jeff Holt
Publisher: 
MAA
Rights: 
MAA

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