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 $[{A_1}, \ldots ,{A_k}] \ne 0$.References
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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