Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A15

Retrieve articles in all journals with MSC: 15A15

Additional Information

PII: S 0002-9939(1975)0376708-9
Keywords: Standard polynomial, digraph, Euler path, skew-symmetric
Article copyright: © Copyright 1975 American Mathematical Society