On the characteristic polynomial, eigenvalues for block tridiagonal matrices

Abstract

Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices. In this paper, we derive specific formulas for characteristic polynomials, and eigenvalues for a class of block tridiagonal matrices. We apply the results to determine the charactristic polynomial of some block Toeplitz symmetric tridiagonal matrices and give the explicit eigenvalues. Particularly, when the blocks are diagonal matrices, the eigenvalues are calculated explicitly.