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

 

Applications of graph theory to matrix theory


Author: Frank W. Owens
Journal: Proc. Amer. Math. Soc. 51 (1975), 242-249
MSC: Primary 15A15
MathSciNet review: 0376708
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Abstract: Let $ {A_1}, \ldots ,{A_k}$ be $ n \times n$ matrices over a commutative ring $ R$ with identity. Graph theoretic methods are established to compute the standard polynomial $ [{A_1}, \ldots ,{A_k}]$. It is proved that if $ k < 2n - 2$, and if the characteristic of $ R$ either is zero or does not divide $ 4I(1/2n) - 2$, where $ I$ denotes the greatest integer function, then there exist $ n \times n$ skew-symmetric matrices $ {A_1}, \ldots ,{A_k}$ such that $ [{A_1}, \ldots ,{A_k}] \ne 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0376708-9
PII: S 0002-9939(1975)0376708-9
Keywords: Standard polynomial, digraph, Euler path, skew-symmetric
Article copyright: © Copyright 1975 American Mathematical Society