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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0376708-9
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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Keywords: Standard polynomial, digraph, Euler path, skew-symmetric
Article copyright: © Copyright 1975 American Mathematical Society