Graphical evaluation of sparse determinants
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- by Daniel Drucker and David M. Goldschmidt PDF
- Proc. Amer. Math. Soc. 77 (1979), 35-39 Request permission
Abstract:
In this paper, we show that the determinant of a matrix with entries in a commutative ring can be recursively computed by use of an associated directed graph whose circuits are assigned weights in the ring. This result provides an efficient means of calculating the determinants of sparse matrices. As an application, we compute the determinants of the Cartan matrices associated to the simple complex Lie algebras.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 35-39
- MSC: Primary 15A15; Secondary 05C20, 17B20
- DOI: https://doi.org/10.1090/S0002-9939-1979-0539626-2
- MathSciNet review: 539626