Bounds for the spectral radius of nonnegative irreducible matrices

Journal of Lanzhou University of Technology ›› 2025, Vol. 51 ›› Issue (5): 163-166.

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Bounds for the spectral radius of nonnegative irreducible matrices

LI Na¹, ZHONG Qin²

1. School of Intelligence Technology, Geely University of China, Chengdu 641423, China;
2. Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China

Received:2023-09-26 Online:2025-10-28 Published:2025-10-25

Abstract

Abstract: Based on the nonzero row sums of nonnegative matrices, the classical Gerschgorin disk theorem and Hölder inequality are applied to estimate the spectral radius of a nonnegative matrix, and the expressions of the upper and lower bounds of the spectral radius of a nonnegative matrix are obtained. The proposed methods have good operability and can get tight upper and lower bounds. Finally, the accuracy of the results is verified by specific arithmetic examples.

Key words: nonnegative matrix, irreducible, spectral radius, upper bound, lower bound

CLC Number:

O151.21

LI Na, ZHONG Qin. Bounds for the spectral radius of nonnegative irreducible matrices[J]. Journal of Lanzhou University of Technology, 2025, 51(5): 163-166.

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Bounds for the spectral radius of nonnegative irreducible matrices

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