Invertibly convergent innite products of matrices
William F. Trench · 1999
The standard denition of convergence of an innite product of scalars is extended to the innite product P= 1=1Bn of k k matrices; that is, P is convergent according to the denition given here if and only if there is an integer N such that Bn is invertible for n>N and P= limn!1 n=NBm is invertible. A family of sucient conditions for this kind of convergence is given, along with examples showing that they have nontrivial applications. c 1999 Elsevier Science B.V. All rights reserved.