Determinants of Block Tridiagonal Matrices

A tridiagonal matrix with entries given by square matrices is a block tridiagonal matrix; the matrix is banded if off-diagonal blocks are upper or lower triangular. Such matrices are of great importance in numerical analysis and physics, and to obtain general properties is of great utility. The blocks of the inverse matrix of a block tridiagonal matrix can be factored in terms of two sets of matrices[10], and decay rates of their matrix elements have been investigated[14]. While the spectral properties of tridiagonal matrices have been under study for a long time, those of tridiagonal block matrices are at a very initial stage[1,2].