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

Qin Zhong and Jie Wu ()
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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

Mathematics, 2025, vol. 13, issue 19, 1-12

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.

Keywords: nonnegative matrix; extended Perron complement; γ-diagonally dominant; product γ-diagonally dominant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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