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

  • M. S. P. Eastham (a1)

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.

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1Eastham, M. S. P.. Asymptotic theory and deficiency indices for differential equations of odd order. Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 263279.
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6Naimark, M. A.. Linear differential operators, Part 2 (London: Harrap, 1968).
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8Yakubovich, V. A. and Starzhinskii, V. M.. Linear differential equations with periodic coefficients, Vol. 1 (New York: Wiley, 1975).

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