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.

Keywords

Quaternion matrices Right eigenvalues Gerschgorin type theorem Location 

Mathematics Subject Classification (2000)

15A21 15A66 
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References

  1. 1.
    Zhuang, W.: The Guide of Quaternion Algebra Theory. Science Press, Beijing (2006), (in Chinese) Google Scholar
  2. 2.
    Wang, Q.: Quaternion transformation and its application on the display-cement analysis of spatial mechanisms. Acta Mech. Sin. 1983(01), 54–61 (1983), (in Chinese) MATHGoogle Scholar
  3. 3.
    Zhang, G.: Commutatively of composition for finite rotations of a rigid body. Acta Mech. Sin. 1982(04), 363–368 (1982), (in Chinese) MATHGoogle Scholar
  4. 4.
    Ran, R., Huang, T.: The recognition of color images based on the singular value decompositions of quaternion matrices. Comput. Sci. 2006(7), 227–229 (2006), (in Chinese) Google Scholar
  5. 5.
    Zhang, F.: Gerschgorin type theorems for quaternionic matrices. Linear Algebra Appl. 424, 139–153 (2007) CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Huang, L.: On left eigenvalues of a quaternionic matrix. Linear Algebra Appl. 323, 105–116 (2001) CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Huang, L.: On two questions about quaternion matrices. Linear Algebra Appl. 318, 79–86 (2000) CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Wu, J.: Distribution and estimation for eigenvalues of real quaternion matrices. Comput. Math. Appl. 55, 1998–2004 (2008) CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Zhang, F.: Quaternions and matrices of quaternions. Linear Algebra Appl. 251, 21–57 (1997) CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Wang, Q.: The general solution to a system of real quaternion matrix equation. Comput. Math. Appl. 49, 665–675 (2005) CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Wu, J., Zou, L., Chen, X., Li, S.: The estimation of eigenvalues of sum, difference, and tensor product of matrices over quaternion division algebra. Linear Algebra Appl. 428, 3023–3033 (2008) CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Cohn, P.M.: Skew Field Constructions. Cambridge University Press, Cambridge (1977) MATHGoogle Scholar
  13. 13.
    Adler, S.L.: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, London (1995) MATHGoogle Scholar
  14. 14.
    Cohn, P.M.: Skew Field-Theory of General Division Rings. Cambridge University Press, Cambridge (1995) Google Scholar
  15. 15.
    Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985) MATHGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2010

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceChongqing Three Gorges UniversityChongqingP.R. China
  2. 2.College of Mathematics and StatisticsChongqing UniversityChongqingP.R. China

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