Year: 2025
Type: article
Abstract: In this article, we study an analogue of a classical result for M-matrices: if T - I is an invertible M-matrix, then both T and I - T-1 are also invertible M-matrices. We extend this implication to a broader class—inverse H-matrices. The expressions T - I and I - T-1 commonly arise in the analysis of matrix stability, convergence of iterative methods, and spectral transformations, making their structural properties important for numerical analysis. We demonstrate that this implication does not generally hold for inverse H-matrices. However, we derive some conditions under which it remains valid. Specifically, we prove that under certain conditions, if T - I is an inverse H-matrix, then T and I - T-1 are also inverse H-matrices. Additionally, we investigate the result in the context of group inverses, showing that it does not hold for group inverse M-matrices and H-matrices.
Institutions: Hasanuddin University, Bandung Institute of Technology
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413961999