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The reconstruction of an hermitian toeplitz matrix with prescribed eigenpairs

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Abstract

This paper concerns the reconstruction of an hermitian Toeplitz matrix with prescribed eigenpairs. Based on the fact that every centrohermitian matrix can be reduced to a real matrix by a simple similarity transformation, the authors first consider the eigenstructure of hermitian Toeplitz matrices and then discuss a related reconstruction problem. The authors show that the dimension of the subspace of hermitian Toeplitz matrices with two given eigenvectors is at least two and independent of the size of the matrix, and the solution of the reconstruction problem of an hermitian Toeplitz matrix with two given eigenpairs is unique.

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410076, China

    Zhongyun Liu & Lu Chen

  2. Department of Mathematics, University of Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Yulin Zhang

Authors
  1. Zhongyun Liu
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  2. Lu Chen
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  3. Yulin Zhang
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Corresponding author

Correspondence to Zhongyun Liu.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant Nos. 10771022 and 10571012, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China under Grant No. 890 [2008], and Major Foundation of Educational Committee of Hunan Province under Grant No. 09A002 [2009]; Portuguese Foundation for Science and Technology (FCT) through the Research Programme POCTI, respectively.

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Liu, Z., Chen, L. & Zhang, Y. The reconstruction of an hermitian toeplitz matrix with prescribed eigenpairs. J Syst Sci Complex 23, 961–970 (2010). https://doi.org/10.1007/s11424-010-0212-1

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  • DOI: https://doi.org/10.1007/s11424-010-0212-1

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