Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-02T20:22:29.779Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.