On the eigenvectors for a class of matrices arising from quasi-derivatives
M. S. P. Eastham · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1984
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.