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On an extension of Fu-Markham matrix theory result to simple Euclidean Jordan algebras

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Abstract

In matrix theory, Fu and Markham showed using majorization technique that if a Hermitian matrix satisfies certain conditions, then the matrix must be block-diagonal. In this paper, we extend this result to the setting of simple Euclidean Jordan algebras by using the Cauchy interlacing theorem and the Schur complement Cauchy interlacing theorem.

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Acknowledgements

We would like to thank the anonymous referees for their very constructive suggestions and comments. The work was supported in part by the National Natural Science Foundation of China (11171018) and the Fundamental Research Funds for the Central Universities (2011JBM306).

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R. China

    Bo Zhong

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China

    Yongqiang Chen

  3. Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, MD, 21210, USA

    Jiyuan Tao

Authors
  1. Bo Zhong
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  2. Yongqiang Chen
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  3. Jiyuan Tao
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Correspondence to Jiyuan Tao.

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Zhong, B., Chen, Y. & Tao, J. On an extension of Fu-Markham matrix theory result to simple Euclidean Jordan algebras. Ann Oper Res 243, 245–248 (2016). https://doi.org/10.1007/s10479-013-1464-7

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  • DOI: https://doi.org/10.1007/s10479-013-1464-7

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