Fundamental equations

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.

Define

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, .

(Q20) And

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Copyright © 2007 Todd Will

Created by
Mathematica (April 14, 2007)