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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximum rank of powers of a matrix of a given pattern


Author: Svatopluk Poljak
Journal: Proc. Amer. Math. Soc. 106 (1989), 1137-1144
MSC: Primary 15A03; Secondary 05C20, 05C38
MathSciNet review: 963575
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Abstract: The pattern of a matrix is the structure of its zero and nonzero entries. For any prescribed pattern we determine the maximum possible rank of each power of a matrix with a given pattern. The approach is based on a combinatorial result that may be of some interest independently.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0963575-5
PII: S 0002-9939(1989)0963575-5
Article copyright: © Copyright 1989 American Mathematical Society