Don’t let Keanu Reeves steal the focus!
This is an excellent tutorial on Singular Value Decomposition (SVD) by Todd Will from UW-La Crosse. I highly recommend it for everybody who deals with Linear Algebra.
http://www.uwlax.edu/faculty/will/svd/index.html
Among other excellent insights, once you read the page on Perpframes, Aligner and Hangers (the 3rd page in that site), you will never see a matrix the same way again. It’s like the, erh, blue pill. (Or is it the red one? 
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