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On Extended Perron Complements of Nonnegative Irreducible γ-Diagonally and Product γ-Diagonally Dominant Matrices

Author

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  • Qin Zhong

    (Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China)

  • Jie Wu

    (College of Computer Science, Chengdu University, Chengdu 610106, China)

Abstract

This study explores the γ-diagonal dominance and product γ-diagonal dominance properties of extended Perron complements. We prove that nonnegative irreducible matrices that are (strictly) γ-diagonally dominant maintain their nonnegativity, irreducibility, and (strictly) γ-diagonal dominance after applying the extended Perron complement operation. Similarly, (strictly) product γ-diagonally dominant nonnegative irreducible matrices also retain these properties under the same operation. Two numerical examples illustrate and validate these theoretical results.

Suggested Citation

  • Qin Zhong & Jie Wu, 2025. "On Extended Perron Complements of Nonnegative Irreducible γ-Diagonally and Product γ-Diagonally Dominant Matrices," Mathematics, MDPI, vol. 13(19), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3221-:d:1766398
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