You just learned that if stretches and sends an orthonormal basis to an orthonormal basis then has an SVD of .
If on the other hand you start with orthonormal bases and and define then you'll know that will stretch and send the orthonormal basis to the orthonormal basis .
In particular you'll know and . These are the FUNDAMENTAL EQUATIONS for an SVD.
You can check that both and are orthonormal bases for . This tells you that you've got an SVD for and that the fundamental equations hold. So, .
Copyright © 2007 Todd Will
Created by Mathematica (April 14, 2007)