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BY 4.0 license Open Access Published by De Gruyter Open Access December 13, 2019

Extensions of the Eneström-Kakeya theorem for matrix polynomials

  • A. Melman EMAIL logo
From the journal Special Matrices


The classical Eneström-Kakeya theorem establishes explicit upper and lower bounds on the zeros of a polynomial with positive coefficients and has been generalized for positive definite matrix polynomials by several authors. Recently, extensions that improve the (scalar) Eneström-Kakeya theorem were obtained with a transparent and unified approach using just a few tools. Here, the same tools are used to generalize these extensions to positive definite matrix polynomials, while at the same time generalizing the tools themselves. In the process, a framework is developed that can naturally generate additional similar results.

MSC 2010: 12D10; 30C15; 65H05


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Received: 2019-08-19
Accepted: 2019-12-03
Published Online: 2019-12-13

© 2019 A. Melman, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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