An Analytical and Applied Study on the Summation Properties of Σ- Strictly Diagonally Dominant Matrices with Numerical Verification

Authors

  • Abear Saed Abo Glida Saed Department of Mathematics, Faculty of Science, University of Alzawia, Alajelat, Libya Author
  • Sana Mohamed Abdulwanis Mohamed Department of Mathematics, Faculty of Education, University of Tripoli, Tripoli, Libya Author

Keywords:

k-subdirect sum, H-matrices, Σ-SDD matrices, overlapping blocks, diagonal dominance

Abstract

In this research, we extend the existing results on subdirect sums of S-strictly diagonally dominant matrices to the more general class of Σ-Strictly Diagonally Dominant (Σ-SDD) matrices. As Σ-SDD matrices form a proper superclass of S-SDD matrices and a subclass of H-matrices, we investigate their structural properties under matrix combination operations. Specifically, we provide a complete characterization of the conditions under which the k-subdirect sum of two Σ-SDD matrices preserves the Σ-SDD property. Furthermore, we establish when the conventional sum of two Σ-SDD matrices remains Σ-SDD. These results broaden the understanding of diagonal dominance under scaling and contribute to the study of matrix stability within hierarchical subclasses of H-matrices.

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Published

2025-12-30

Issue

Volume 3, Issue 4, 2025

Section

Applied Sciences Theme

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Abear Saed Abo Glida Saed, & Sana Mohamed Abdulwanis Mohamed. (2025). An Analytical and Applied Study on the Summation Properties of Σ- Strictly Diagonally Dominant Matrices with Numerical Verification. Afro-Asian Journal of Scientific Research (AAJSR), 3(4), 268-273. https://aajsr.com/index.php/aajsr/article/view/725