On determinantal recurrence relations of banded matrices

Abstract

We provide an algorithm based on a less-known result about recurrence relations for the determinants of banded matrices. As a consequence, we prove recent conjectures on the determinants of particular classes of pentadiagonal matrices and simple alternative proofs for other results.

The determinants of certain double banded (0,1) Toeplitz matrices

“…It is worth indicating that here we need the precondition that n c + 6, or equivalently, n max{c + 6, 6 − c}, which guarantees the using of Theorem 1 to the three determinants ∆ 1 ( * , * ). Then the expression of ∆ 2 n, n+c As to the remaining two cases n = c + 2 and n = c + 4, they just correspond to the two conjectures proposed in [2], which were confirmed in [6] (see also [1,4,5,7]. Following the notations in the paper, they claim that…”