Factorization of matrix functions and their inverses via power product expansions (Q1019727)

The author studies the conversion of a power series with matrix coefficients into an infinite product of certain elementary matrix functions. He also analyses the expansion of a power series with matrix coefficients as the inverse of an infinite product of elementary factors. Each elementary factor is the sum of the identity matrix and a certain matrix coefficient multiplied by a certain power of the variable. The two expansions provide representations of a matrix function and its inverse by infinite products of elementary factors. Also, estimates on the domain of convergence of the infinite products are given.