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Inequalities for central moments and spreads of matrices

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Abstract

We derive some inequalities involving first four central moments of discrete and continuous distributions. Bounds for the eigenvalues and spread of a matrix are obtained when all its eigenvalues are real. Likewise, we discuss bounds for the roots and span of a polynomial equation.

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Acknowledgements

The authors are grateful to Prof. Rajendra Bhatia for the useful discussions and suggestions, and first author thanks Ashoka University for a visit in January 2019. The second author thankful to SERB-DST, the Government of India, for support financially under the sanction number EEQ/2019/000593. The support of UGC-SAP is acknowledged. The authors would like to thank the anonymous referee for many helpful and constructive suggestions to an earlier version of this paper, which results in a significant improvement.

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Authors and Affiliations

  1. Department of Mathematics, Himachal Pradesh University, Shimla, 171005, India

    R. Sharma, R. Saini & Purnima Devi

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

    R. Kumar

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  1. R. Sharma
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  2. R. Kumar
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  3. R. Saini
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  4. Purnima Devi
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Corresponding author

Correspondence to R. Kumar.

Additional information

Communicated by Qing-Wen Wang.

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Sharma, R., Kumar, R., Saini, R. et al. Inequalities for central moments and spreads of matrices. Ann. Funct. Anal. 11, 815–830 (2020). https://doi.org/10.1007/s43034-020-00056-y

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  • DOI: https://doi.org/10.1007/s43034-020-00056-y

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