A Recursive Relation for the Determinant of a Pentadiagonal Matrix

Abstract

A recursive relation is developed for the determinant of a pentadiagonal matrix $S$ which satisfies $s_{i,j} \neq 0$ for $|i-j|=1$. When $S$ is symmetric, one has a six-term recursive relation. An example is given to illustrate its use in the computation of eigenvalues.