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An Algorithm for Coneigenvalues and Coneigenvectors of Quaternion Matrices

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Abstract

Coneigenvalues and coneigenvectors are the most important quantities related to consimilarity tranformations of quaternion matrices. By mean of complex representation method, we characterize the relations between principle right coneigenvalues of a quaternion matrix and eigenvalues of corresponding complex representation matrix. In addition, an algorithm based on the complex representation is described for computing the coneigenvalues and coneigenvectors of quaternion matrices. In the end an example is given to illustrate the validity of our algorithm.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China

    Sitao Ling

  2. College of Mathematics and Information, Ludong University, Yantai, 264025, P.R. China

    Xuehan Cheng

  3. College of Science, Linyi University, Linyi, 276005, P.R. China

    Tongsong Jiang

  4. College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao, 266510, P.R. China

    Tongsong Jiang

Authors
  1. Sitao Ling
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  2. Xuehan Cheng
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  3. Tongsong Jiang
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Corresponding author

Correspondence to Tongsong Jiang.

Additional information

This paper is supported in part by the National Natural Science Foundations of China (11301529, 11201193), and the Fundamental Research Funds for the Central Universities under grant 2012QNB22.

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Ling, S., Cheng, X. & Jiang, T. An Algorithm for Coneigenvalues and Coneigenvectors of Quaternion Matrices. Adv. Appl. Clifford Algebras 25, 377–384 (2015). https://doi.org/10.1007/s00006-014-0496-7

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  • DOI: https://doi.org/10.1007/s00006-014-0496-7

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