Skip to main content
SpringerLink
Log in

Algebraic Methods for Condiagonalization Under Consimilarity of Quaternion Matrices in Quaternionic Quantum Mechanics

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

By means of complex representation and real representation of quaternion matrices, paper [7] studied the problem of diagonalization of quaternion matrices. This paper introduces two new complex representation and real representation of quaternion matrices, studies the problem of condiagonalization under consimilarity of quaternion matrices, and gives two algebraic methods for the condiagonalization under consimilarity of quaternion matrices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sakurai, J. J, Modern Quantum Mechanics. Menlo Park, CA: Benjamin/cummings, 1985.

  2. Shankar, R, Principles of Quantum Mechanics. Plenum Publishing Corporation, Inc., 1984.

  3. Weinberg S: The Quantum Theory of Fields. Volume 1. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  4. Adler S.L: Quaternionic Quantum Field Theory. Phys. Rev. Lett. 55, 783–786 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  5. Adler S.L.: Quaternionic Quantum Field Theory. Comm. Math. Phys. 104, 611–656 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Adler S.L: Quaternionic Quantum Mechanics and Quantum Fields. Oxford University Press, New York (1995)

    MATH  Google Scholar 

  7. Jiang T: Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory. J. Math. Phys. 46, 052106 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  8. Jiang T.: An algorithm for eigenvalues and eigenvectors of quaternion matrices in quaternionic quantum mechanics. J. Math. Phys. 45, 3334–3338 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Huang L: Consimilarity of quaternion matrices and complex matrices. Linear Algebra Appl. 331, 21–30 (2001)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Linyi University, Linyi, 276005, P.R. China

    Tongsong Jiang

  2. Department of Computer Science and Technology, Shandong University, Jinan, 250100, P.R. China

    Tongsong Jiang

  3. Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China

    Sitao Ling

Authors
  1. Tongsong Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sitao Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sitao Ling.

Additional information

Tongsong Jiang: This author is supported in part by the National Natural Science Foundation of China under grant 10671086 and the Shandong Natural Science Foundation under grant ZR2010AM014.

Sitao Ling: This author is supported in part by the National Natural Science Foundation of China under grant 11171343, 11201193 and the Fundamental Research Funds for the Central Universities under grant 2012QNB22.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, T., Ling, S. Algebraic Methods for Condiagonalization Under Consimilarity of Quaternion Matrices in Quaternionic Quantum Mechanics. Adv. Appl. Clifford Algebras 23, 405–415 (2013). https://doi.org/10.1007/s00006-013-0379-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-013-0379-3

Keywords

Search

Navigation