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

Author:

Eastham M. S. P.

Abstract

SynopsisLet 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. Asymptotic methods in the theory of one-dimensional singular differential operators;Fedorjuk;Trans. Moscow Math. Soc.,1966

2. Generalized symmetric ordinary differential expressions I: the general theory;Everitt;Nieuw Arch. Wisk,1979

3. Asymptotic Theory and Deficiency Indices for Higher-Order Self-Adjoint Differential Equations

4. Asymptotic behaviour of solutions of ordinary linear differential equations of the n-th order;Fedorjuk;Soviet Math.,1965

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