On the Investigation of a Linear Eigenvalue Problem for Matrices

Abstract

This paper investigates the properties of eigenvalues and eigenvectors of the problem $Jy + \lambda Ry = (1/\lambda ) Cy$, where $J$ is a "tridiagonal'' real symmetric matrix and $R$ and $C$ are positive diagonal matrices. The results obtained are used to solve the corresponding system of differential equations with boundary and initial conditions.