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 be matrices over a commutative ring with identity. Graph theoretic methods are established to compute the standard polynomial . It is proved that if , and if the characteristic of either is zero or does not divide , where denotes the greatest integer function, then there exist skew-symmetric matrices such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0376708-9

Keywords:
Standard polynomial,
digraph,
Euler path,
skew-symmetric

Article copyright:
© Copyright 1975
American Mathematical Society