ON CONDITIONS FOR MATRICES T SUCH THAT T-I AND I-T^(-1) ARE INVERSE H-MATRICES*

  • Jeriko Gormantara Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin, Indonesia https://orcid.org/0000-0001-9691-1260
  • Hanni Garminia Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0009-0001-8949-4961
  • Amir Kamal Amir Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin, Indonesia https://orcid.org/0000-0003-1539-4922
  • Evan Ramdan Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Hasanuddin, Indonesia https://orcid.org/0009-0007-2541-7207
Keywords: Group Inverse, H-Matrix, Inverse H-Matrix, M-Matrix

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.

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Published
2025-09-01
How to Cite
[1]
J. Gormantara, H. Garminia, A. K. Amir, and E. Ramdan, “ON CONDITIONS FOR MATRICES T SUCH THAT T-I AND I-T^(-1) ARE INVERSE H-MATRICES*”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2953-2962, Sep. 2025.