Some new inequalities for nonnegative matrices involving Schur product

Qin Zhong; Qin Zhong

doi:10.3934/math.20231518

AIMS Mathematics

2023, Volume 8, Issue 12: 29667-29680. doi: 10.3934/math.20231518

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Some new inequalities for nonnegative matrices involving Schur product

Qin Zhong ^,

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

Received: 16 September 2023 Revised: 23 October 2023 Accepted: 24 October 2023 Published: 01 November 2023
MSC : 15A47

In this study, we focused on the spectral radius of the Schur product. Two new types of the upper bound of $ \rho \left({M \circ N} \right) $, which is the spectral radius of the Schur product of two matrices $ M, N $ with nonnegative elements, were established using the Hölder inequality and eigenvalue inclusion theorem. In addition, the obtained new type upper bounds were compared with the classical conclusions. Numerical examples demonstrated that the new type of upper formulas improved the result of Johnson and Horn effectively in some cases, and were sharper than other existing results.
- nonnegative matrix,
- Schur product,
- spectral radius,
- irreducible
Citation: Qin Zhong. Some new inequalities for nonnegative matrices involving Schur product[J]. AIMS Mathematics, 2023, 8(12): 29667-29680. doi: 10.3934/math.20231518

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Abstract

In this study, we focused on the spectral radius of the Schur product. Two new types of the upper bound of $ \rho \left({M \circ N} \right) $, which is the spectral radius of the Schur product of two matrices $ M, N $ with nonnegative elements, were established using the Hölder inequality and eigenvalue inclusion theorem. In addition, the obtained new type upper bounds were compared with the classical conclusions. Numerical examples demonstrated that the new type of upper formulas improved the result of Johnson and Horn effectively in some cases, and were sharper than other existing results.

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