Invertibly convergent infinite products of matrices

摘要

The standard definition of convergence of an infinite product of scalars is extended to the infinite product P = Πn=1∞Bn of k × k matrices; that is, P is convergent according to the definition given here if and only if there is an integer N such that Bn is invertible for n⩾N and P=limn→∞ Πm=NnBm is invertible. A family of sufficient conditions for this kind of convergence is given, along with examples showing that they have nontrivial applications.