This process can done by 
This process can done by summing semisimple and nilpotent parts in an example of it named for Jordan and Chevalley. The normal equations method for solving least-squares problems uses an efficient one of these processes named for Cholesky. For M that is m by n, this process can be performed by [read slowly] finding Σ ["sigma"], whose diagonal entries are the (*) singular values of M, then finding m by m U and n by n V* ["v-star"], which are both unitary; M then equals U times Σ times V*. For 10 points, name this process in which a matrix is expressed as a product of other matrices.
This process can done by summing semisimple and nilpotent parts in an example of it named for Jordan and Chevalley.
matrix decomposition [accept any variety of decomposition, such as orthogonal decomposition, QR decomposition, or singular value decomposition; accept matrix factorization; prompt on factorization]