Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-20T00:36:36.672Z Has data issue: false hasContentIssue false
  • English
  • Français

On the eigenvectors for a class of matrices arising from quasi-derivatives

Published online by Cambridge University Press:  14 November 2011

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Chelsea College (University of London), London SW10 OUA
Get access Rights & Permissions [Opens in a new window]

Synopsis

Let A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 73 - 78
Copyright
Copyright © Royal Society of Edinburgh 1984

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

1Eastham, M. S. P.. Asymptotic theory and deficiency indices for differential equations of odd order. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 263–279.CrossRefGoogle Scholar
2Eastham, M. S. P. and Grudniewicz, C. G. M.. Asymptotic theory and deficiency indices for higher-order self-adjoint differential equations. J. London Math. Soc. 24 (1981), 255–271.CrossRefGoogle Scholar
3Everitt, W. N. and Zettl, A.. Generalized symmetric ordinary differential expressions I: the general theory. Nieuw Arch. Wisk. 27 (1979), 363–397.Google Scholar
4Fedorjuk, M. V.. Asymptotic behaviour of solutions of ordinary linear differential equations of the n-th order. Soviet Math. 6 (1965), 1528–1530.Google Scholar
5Fedorjuk, M. V.. Asymptotic methods in the theory of one-dimensional singular differential operators. Trans. Moscow Math. Soc. 15 (1966), 333–386 in the Amer. Math. Soc. translation.Google Scholar
6Naimark, M. A.. Linear differential operators, Part 2 (London: Harrap, 1968).Google Scholar
7Pease, M. C.. Methods of matrix algebra (New York: Academic Press, 1965).Google Scholar
8Yakubovich, V. A. and Starzhinskii, V. M.. Linear differential equations with periodic coefficients, Vol. 1 (New York: Wiley, 1975).Google Scholar