Isospectral Flows and Abstract Matrix Factorizations * Moody T . Chu ? and Larry

A general framework for constructing isospectral flows in the space gl(n) of n by n matrices is proposed. Depending upon how gl(n) is split, this framework gives rise to different types of abstract matrix factorizations. When sampled at integer times, these flows naturally define special iterative processes, and each flow is associated with the sequence generated by the corresponding abstract factorization. The proposed theory unifies as special cases the well-known matrix decomposition techniques used in numerical linear algebra and is likely to offer a broader approach to the general matrix factorization problem.