Matrix factorizations and their perturbations

There are several ways in which a matrix can be factorized as a product of two special matrices. These factorizations are often used in numerical analysis, and many perturbation bounds useful in such analysis have been proved by various authors. In this paper a simple method which leads to these results and several new ones is discussed. In the last section related results on the Lipschitz continuity of the matrix absolute value are surveyed