Abstract
In this paper, we discuss how unital positive linear functionals can be used to obtain intervals for the arithmetic mean of extreme eigenvalues of a Hermitian matrix. Furthermore, we derive some intervals for the real numbers and give their interesting applications in matrix theory and polynomial theory.
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Acknowledgements
The authors would like to thank learned referee for their valuable remarks and suggestions to an earlier version of this paper, which results in a significant improvement. The research of first author is supported by the University Grants Commission (UGC), Government of India. The second author is supported in part by the Empowerment and Equity Opportunities for Excellence in Science (EEQ/2019/000593) by SERB (DST), Government of India.
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Verma, M., Kumar, R. Inequalities involving eigenvalues and positive linear functionals. J Anal (2024). https://doi.org/10.1007/s41478-024-00724-5
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DOI: https://doi.org/10.1007/s41478-024-00724-5