Some new bounds on the spectral radius of nonnegative matrices

Maria Adam; Dimitra Aggeli; Aikaterini Aretaki; Maria Adam; Dimitra Aggeli; Aikaterini Aretaki

doi:10.3934/math.2020047

AIMS Mathematics

2020, Volume 5, Issue 1: 701-716. doi: 10.3934/math.2020047

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Research article

Some new bounds on the spectral radius of nonnegative matrices

Department of Computer Science and Biomedical Informatics, University of Thessaly

Received: 01 August 2019 Accepted: 02 December 2019 Published: 19 December 2019
MSC : 15A18, 15A42, 05C50

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.
- nonnegative matrix,
- spectral radius,
- row sum,
- 2-row sum,
- average 2-row sum,
- signless Laplacian matrix
Citation: Maria Adam, Dimitra Aggeli, Aikaterini Aretaki. Some new bounds on the spectral radius of nonnegative matrices[J]. AIMS Mathematics, 2020, 5(1): 701-716. doi: 10.3934/math.2020047

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Abstract

In this paper, we determine some new bounds for the spectral radius of a nonnegative matrix with respect to a new defined quantity, which can be considered as an average of average 2-row sums. The new formulas extend previous results using the row sums and the average 2-row sums of a nonnegative matrix. We also characterize the equality cases of the bounds if the matrix is irreducible and we provide illustrative examples comparing with the existing bounds.

References

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