Section 4.6

I would have liked to see a proof of the statement that said If A is real, then so are U and V (which are then orthogonal matrices) for Theorem 4.6 (Singular Value Decomposition). I'm having a hard time believing that statement without some sort of proof to it. I also don't completely understand what a singular vector is and what its application is. I really found Example 4.6 to be very intersting. Actually this example really helped me a lot to see how SVD compression would work and I am really surprised on the output and MatLab's ability to perform this.