Groups of banded matrices with banded inverses
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Proceedings of the American Mathematical Society
American Mathematical Society
Strang, Gilbert. “Groups of banded matrices with banded inverses.” Proceedings of the American Mathematical Society 139.12 (2011): 4255-4264.
Author's final manuscript