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 
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]