On the theory of a certain class of quadratic pencils of matrices and its applications

This paper is devoted to the study of the properties of eigenvalues and eigenvectors of quadratic pencil ?2C - ?R - J, where C is a positive diagonal matrix, R is an arbitrary real diagonal matrix, J is a "tridiagonal" real symmetric and positive matrix. The obtained results are then used to solve the corresponding system of differential equations with boundary and initial conditions. © TÜBİTAK