Groups of banded matrices with banded inverses

Abstract

A product A=F[subscript 1]...F[subscript N] of invertible block-diagonal matrices will be banded with a banded inverse. We establish this factorization with the number N controlled by the bandwidths w and not by the matrix size n. When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors F[subscript i] have w=1 and generate that corresponding group. In the case of infinite matrices, conjectures remain open.