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Some inequalities related to eigenvalues

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Abstract

In this paper, we discuss inequalities involving the extreme eigenvalues and the spread of a matrix, which, in turn, can be used to obtain bounds for the extreme eigenvalues of an \(n\times n\) complex matrix when all of its eigenvalues are real. We derive an upper bound for the spread of an \(n\times n\) complex matrix. Further, we present some inequalities for the spectral radius of a matrix. Finally, we illustrate some numerical examples to show the effectiveness of our results.

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Acknowledgements

The authors would like to thank the anonymous reviewer and the editor for their valuable comments and suggestions, which improved the quality of the manuscript. This work was supported by the Science and Engineering Research Board, India, Grant no. EEQ/2019/000593.

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Authors and Affiliations

  1. Department of Mathematics, Dr B R Ambedkar National Institute of Technology Jalandhar, Punjab, 144011, India

    Ravinder Kumar & Vidhi Bhatia

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  1. Ravinder Kumar
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  2. Vidhi Bhatia
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Correspondence to Ravinder Kumar.

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Communicated by Kenneth Berenhaut.

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Kumar, R., Bhatia, V. Some inequalities related to eigenvalues. Adv. Oper. Theory 7, 31 (2022). https://doi.org/10.1007/s43036-022-00193-2

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  • DOI: https://doi.org/10.1007/s43036-022-00193-2

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