An optimal bound for inverses of triangular matrices with monotone entries

Abstract

This article provides a new bound for 1-norms of inverses of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality established in Vecchio and Mallik [Bounds on the inverses of non-negative lower triangular Toeplitz matrices with monotonicity properties, Linear Multilinear Alg., 55 (2007), pp. 365–379]. The results are shown to be in a sense best possible under the given constraints.

Keywords:

• inverse matrix
• monotone entries
• triangular matrix
• recurrence relations
• optimal bound

AMS Subject Classifications::

• 15A09
• 39A10
• 15A57
• 15A60