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A Simple Test for the Reality and Sign of the Roots of Two Determinantal Equations of High Degree

Published online by Cambridge University Press:  03 November 2016

Extract

Twice in the course of some work on chemical kinetics it became necessary to determine the type of the solution to a generalised set of any number of first order simultaneous differential equations. The problem reduced in each case to a question of the reality and sign of the roots of the auxiliary equation, which was, of course, determinantal in form. The required information could be deduced from long-established theorems on the roots of symmetric and skew-symmetric determinantal equations, but the following proofs, which are on a much simpler level, may be of interest.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1950

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References

* (Equation I.). Margaret J. Moore, Trans. Faraday Soc., XLV, 12, 1098, 1949. (Equation 11.). K. G. Denbigh, M. J Hicks (Moore), F. M. Page, Trans. Faraday Soc., XLIV, 7, 479, 1948.