Singular value decomposition (SVD)
	SVD decomposes any mxn matrix A as Properties • Σ is a diagonal matrix containing the eigenvalues of ATA – known as “singular values” of A – diagonal entries are sorted from largest to smallest • columns of U are eigenvectors of AAT • columns of V are eigenvectors of ATA If A is singular (e.g., has rank 3) • only first 3 singular values are nonzero • we can throw away all but first 3 columns of U and V • Choose M’ = U’,  S’ = Σ’V’T