New inequalities on the Hadamard product of nonnegative matrices

Qin Zhong; Ling Li; Gufang Mou; Qin Zhong; Ling Li; Gufang Mou

doi:10.3934/math.2025598

AIMS Mathematics

2025, Volume 10, Issue 6: 13330-13342. doi: 10.3934/math.2025598

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Research article

New inequalities on the Hadamard product of nonnegative matrices

Qin Zhong ^{1
,
,},
Ling Li ^{2
,
,},
Gufang Mou ³

1.
Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China
2.
School of Big Data and Artificial Intelligence, Chengdu Technological University, Chengdu 611730, China
3.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China

Received: 04 March 2025 Revised: 15 May 2025 Accepted: 05 June 2025 Published: 10 June 2025
MSC : 15A18, 15A42, 15A48

Several novel upper bounds for the spectral radius of the Hadamard product of two nonnegative matrices are presented by leveraging spectral radius properties and the Cauchy-Schwarz inequality. The derived bounds incorporate the maximum values of the non-diagonal elements in each row of the nonnegative matrices. Furthermore, concrete examples are presented to illustrate our results are more accurate than existing relevant results.
- irreducible,
- Hadamard product,
- nonnegative matrix,
- spectral radius
Citation: Qin Zhong, Ling Li, Gufang Mou. New inequalities on the Hadamard product of nonnegative matrices[J]. AIMS Mathematics, 2025, 10(6): 13330-13342. doi: 10.3934/math.2025598

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Abstract

Several novel upper bounds for the spectral radius of the Hadamard product of two nonnegative matrices are presented by leveraging spectral radius properties and the Cauchy-Schwarz inequality. The derived bounds incorporate the maximum values of the non-diagonal elements in each row of the nonnegative matrices. Furthermore, concrete examples are presented to illustrate our results are more accurate than existing relevant results.

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