Singular value decomposition and least squares solutions

Let A be a real m×n matrix with m≧n. It is well known (cf. [4]) that $A = U\sum {V^T} (1) where ${U^T}U = {V^T}V = V{V^T} = {I_n}{\text{ and }}\sum {\text{ = diag(}}{\sigma _{\text{1}}}{\text{,}} \ldots {\text{,}}{\sigma _n}{\text{)}}{\text{.}} The matrix U consists of n orthonormalized eigenvectors associated with the n largest eigenvalues of AA T , and the matrix V consists of the orthonormalized eigenvectors of A T A....