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The book "Numerical Linear Algebra" by Trefethan Trefethen and Bau, also introduces the SVD in this way. The relevant chapters (4 and 5) seem to be complete in Google books. The exposition is not tainted by the 'numerical' in the title.

I don't understand why the SVN isn't given more emphasis in standard introductions to linear algebra. It seems to give a good intuitive decomposition of a linear operator. I would expect it to be a useful theoretical tool even if numerical issues are not being considered.
show/hide this revision's text 1

The book "Numerical Linear Algebra" by Trefethan and Bau, also introduces the SVD in this way. The relevant chapters (4 and 5) seem to be complete in Google books. The exposition is not tainted by the 'numerical' in the title.

I don't understand why the SVN isn't given more emphasis in standard introductions to linear algebra. It seems to give a good intuitive decomposition of a linear operator. I would expect it to be a useful theoretical tool even if numerical issues are not being considered.