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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Applications of graph theory to matrix theory
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by Frank W. Owens PDF
Proc. Amer. Math. Soc. 51 (1975), 242-249 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • 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