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Invertibly convergent infinite products of matrices

✍ Scribed by William F. Trench

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
338 KB
Volume
101
Category
Article
ISSN
0377-0427

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✦ Synopsis

The standard definition of convergence of an infinite product of scalars is extended to the infinite product P = II~B, of k x 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 = lim,~ II~,=uBm is invertible. A family of sufficient conditions for this kind of convergence is given, along with examples showing that they have nontrivial applications. (~) 1999 Elsevier Science B.V. All rights reserved.

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