The full assignment is



8.3.3 a, c

8.3.15 a, c, g

8.4.1 b,d

8.5.1 e


In 8.5.1 e I’d like you not just to find the singular values, but also the eigenvectors and Q matrices, and verify that Q Sigma Q^T = A where you use the appropriate Q matrix in the appropriate places.  Also find the “compressed image” that results when you discard the smaller singular value and calculate Qcompressed Sigmacompressed Qcompressed^T; how does it compare to A?  Find the pseudoinverse A^+ = Q Sigma^-1 Q^T, and calculate the products AA^+ and A^+A (one of which will be an identity matrix, I think).  Then find the “compressed pseudoinverseA^+compressed = Qcompressed Sigmacompressed^-1 Qcompressed^T.  How does A times the compressed pseudoinverse look (whichever order gave I), compared to the identity?


That should be loads of fun!