[1] Zhou Jianhua,. Simultaneous diagonalization of two quaternion matrices [J]. Journal of Southeast University (English Edition), 2003, 19 (2): 178-181. [doi:10.3969/j.issn.1003-7985.2003.02.017]
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Simultaneous diagonalization of two quaternion matrices(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 19
- Issue:
- 2003 2
- Page:
- 178-181
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2003-06-30
Info
- Title:
- Simultaneous diagonalization of two quaternion matrices
- Author(s):
- Zhou Jianhua
- Department of Mathematics, Southeast University, Nanjing 210096, China
- PACS:
- O151.21
- DOI:
- 10.3969/j.issn.1003-7985.2003.02.017
- Abstract:
- The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed. The problem is reduced to a parallel one on complex matrices by using the complex adjoint matrix related to each quaternion matrix. It is proved that any two semi-positive definite Hermitian quaternion matrices can be simultaneously diagonalized by congruence.
References:
[1] Wolf L A. Similarity of matrices in which the elements are real quaternions[J]. Bull Amer Math Soc, 1936, 42(2):737-743.
[2] Adler S L. Quaternionic quantum and quantum fields[M]. + New York: Oxford University Press, 1994.
[3] Finkelstein D, Jauch J M, Speiser D. Note on quaternion quantum mechanics[J]. CERN, 1959, 59(9):59-107.
[4] Zhang F. Quaternions and matrices of quaternions[J]. Linear Algebra and Its Application, 1997, 251(2):21-57.
[5] Brenner J L. Matrices of quaterions[J]. Pacific J Math, 1951, 1(2):329-335.
Memo
- Memo:
- Biography: Zhou Jianhua(1962—), male, associate professor, jhzhou@seu.edu.cn.
Last Update: 2003-06-20