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A New Estimation for Eigenvalues of Matrix Power Functions

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Abstract

We give an estimation for the eigenvalues of matrix power functions. In particular, it has been shown that

$$\lambda({(A+B)^p})\leq\lambda({2^{p-1}}({A^p}+{B^p}-\gamma I))\;(P \geq2)$$

for all positive semi-definite matrices A, B, where γ is a positive constant. This provides a sharper bound for the known estimation for eigenvalues.

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Acknowledgement

The authors would like to thank the referee for careful reading of the manuscript and useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P. O. Box 1339, Bojnord, 94531, Iran

    M. Kian

  2. Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    M. Bakherad

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  1. M. Kian
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  2. M. Bakherad
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Correspondence to M. Kian.

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Kian, M., Bakherad, M. A New Estimation for Eigenvalues of Matrix Power Functions. Anal Math 45, 527–534 (2019). https://doi.org/10.1007/s10476-019-0912-2

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  • DOI: https://doi.org/10.1007/s10476-019-0912-2

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