On the Convergence to Zero of Infinite Products of Interval Matrices
β Scribed by Guu, Sy-Ming; Pang, Chin-Tzong
- Book ID
- 118216031
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2003
- Tongue
- English
- Weight
- 173 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0895-4798
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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 i
We derive a necessary and sufficient criterion for the convergence of powers of interval matrices [A] to a limit which may differ from O. Generalizing former results we allow now the absolute value |[A]| of [A] to be reducible with minor additional restrictions.
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 Γ 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