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On the Exponent of a Primitive, Nearly Reducible Matrix

โœ Scribed by Brualdi, Richard A.; Ross, Jeffrey A.


Book ID
118069265
Publisher
INFORMS
Year
1980
Tongue
English
Weight
609 KB
Volume
5
Category
Article
ISSN
0364-765X

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On the exponent of a primitive matrix co
โœ LeRoy B. Beasley; Steve Kirkland ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 713 KB

For a primitive matrix A of order n + k having a primitive submatrix of order 71, we prove that the exponent of A is at most (n -1)" + 2k + 1. We characterize those matrices attaining the bound in terms of their directed graphs, and explicitly describe those graphs for the case that k < 2n.