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Invertibly convergent infinite products of matrices, with applications to difference equations

โœ Scribed by W.F. Trench

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
335 KB
Volume
30
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

The standard definition of convergence of an infinite product of scalars is extended co B

to the infinite product P = ~m=l m of k ร— k matrices; that is, P is convergent according to the definition given here if and only if there is an integer N such that Bm is invertible for m > N and P = limn~co I]nm=N(I + Am) is invertible. Sufficient conditions for this kind of convergence are given. Some of the results seem to be new even for infinite products of scalars. The results are derived by considering related systems of difference equations, and have implications concerning the asymptotic behavior of solutions of these systems.

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