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Location for the right eigenvalues of quaternion matrices

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Abstract

This paper aims to discuss the location for right eigenvalues of quaternion matrices. We will present some different Gerschgorin type theorems for right eigenvalues of quaternion matrices, based on the Gerschgorin type theorem for right eigenvalues of quaternion matrices (Zhang in Linear Algebra Appl. 424:139–153, 2007), which are used to locate the right eigenvalues of quaternion matrices. We shall conclude this paper with some easily computed regions which are guaranteed to include the right eigenvalues of quaternion matrices in 4D spaces.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing, 404000, P.R. China

    Limin Zou & Youyi Jiang

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 400044, P.R. China

    Limin Zou & Junliang Wu

Authors
  1. Limin Zou
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  2. Youyi Jiang
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  3. Junliang Wu
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Corresponding author

Correspondence to Limin Zou.

Additional information

This research was supported by National Natural Science Foundations of China (No. 70872123), Natural Science Foundation of Chongqing Municipal Education Commission (No. KJ101108), and Scientific Research Project of Chongqing Three Gorges University (No. 10ZD-16).

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Zou, L., Jiang, Y. & Wu, J. Location for the right eigenvalues of quaternion matrices. J. Appl. Math. Comput. 38, 71–83 (2012). https://doi.org/10.1007/s12190-010-0464-x

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  • DOI: https://doi.org/10.1007/s12190-010-0464-x

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