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An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications

Author

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  • Tongsong Jiang
  • Xuehan Cheng
  • Sitao Ling

Abstract

This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.

Suggested Citation

  • Tongsong Jiang & Xuehan Cheng & Sitao Ling, 2014. "An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, September.
    • Handle: RePEc:hin:jnljam:795203
    DOI: 10.1155/2014/795203
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    Cited by:

    1. Song, Guangjing & Yu, Shaowen, 2018. "Nonnegative definite and Re-nonnegative definite solutions to a system of matrix equations with statistical applications," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 828-841.

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