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Reducible sign k-potent sign pattern matrices

✍ Scribed by Jeffrey Stuart

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
151 KB
Volume
294
Category
Article
ISSN
0024-3795

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✦ Synopsis

The sign pattern matrix A is called sign k-potent if k is the smallest positive integer such that e k1 eX The structure of irreducible, sign k-potent pattern matrices was characterized by Stuart et al. (J. Stuart, C. Eschenbach, S. Kirkland, Linear Algebra Appl. 294 (1999) 85Β±92). We extend those results to the reducible case, providing necessary conditions that characterize the structure of each o-diagonal block of the Frobenius normal form of a reducible, sign k-potent matrix.

πŸ“œ SIMILAR VOLUMES

Irreducible sign k-potent sign pattern m
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✍ Jeffrey Stuart; Carolyn Eschenbach; Steve Kirkland πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 94 KB

The sign pattern matrix A is called sign k-potent if k is the smallest positive integer for which e k1 eX We characterize the irreducible pattern matrices that are sign k-potent and provide a canonical form for such matrices.

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A sign pattern is said to be potentially nilpotent if it allows nilpotence. In this paper, a number of qualitative necessary or sufficient conditions for a sign pattern to allow nilpotence are established. The sign patterns that allow nilpotence of index 2 are investigated. For orders up to 3, poten