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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Right linear map preserving the left spectrum of 2x2 quaternion matrices; pp. 378–386

(Full article in PDF format) https://doi.org/10.3176/proc.2018.4.08


Authors

Deyu Duan, Xiang Gong, Geng Yuan, Fahui Zhai

Abstract

In this paper, the form of a right linear map preserving the left spectrum of quaternion matrices of order 2 is characterized. The obtained conclusion is different from the classical results of the linear map preserving eigenvalues of complex matrices.

Keywords

linear preserving map, quaternion matrix, left spectrum.

References

1. Farenick , D. R. and Pidkowich , B. A. F. The spectral theorem in quaternions. Linear Algebra Appl. , 2003 , 371 , 75–102.
https://doi.org/10.1016/S0024-3795(03)00420-8

2. Huang , L. P. and So , W. On left eigenvalues of a quaternionic matrix. Linear Algebra Appl. , 2001 , 323 , 105–116.
https://doi.org/10.1016/S0024-3795(00)00246-9

3. Jafarian , A. A. A survey of invertibility and spectrum preserving linear maps. Bull. Iran. Math. Soc. , 2009 , 2 , 1–10.

4. Jafarian , A. A. and Sourour , A. R. Spectrum-preserving linear maps. J. Funct. Anal. , 1986 , 66 , 255–261.
https://doi.org/10.1016/0022-1236(86)90073-X

5. Li , C. K. and Tsing , N. K. Linear preserver problems: a brief introduction and some special techniques. Linear Algebra Appl. , 1992 , 162–164 , 217–235.
https://doi.org/10.1016/0024-3795(92)90377-M

6. Marcus , M. Linear transformations on matrices. J. Res. Nat. Bur. Standards Sect. B. , 1971 , 75B , 107–113.
https://doi.org/10.6028/jres.075B.008

7. Marcus , M. and Moyls , B. N. Linear transformations on algebras of matrices. Canad. J. Math. , 1959 , 11 , 61–66.
https://doi.org/10.4153/CJM-1959-008-0
https://doi.org/10.4153/CJM-1959-039-4

8. Pierce , S. A survey of linear preserver problems. Linear Multilinear Al. , 1992 , 33 , 1–129.
https://doi.org/10.1080/03081089208818176

9. Rodman , L. Topics in Quaternion Linear Algebra. Princeton Univ. Press , Princeton , USA , 2014.

10. So , W. Qnaternionic left eigenvalue problem. Southeast Asian Bull. Math. , 2005 , 29 , 555–565.

11. Sourour , A. R. Three linear perserver problems. In Mathematics and the 21st Century. World Sci. Publ. , London , 2001 , 211–221.
https://doi.org/10.1142/9789812810243_0017

12. Siu , L. S. A Study of Polynomials , Determinants , Eigenvalues and Numerical Ranges Over Quaternions. M. Phil. thesis , University of Hong Kong , 1997.

13. Wood , R. M. W. Quaternionic eigenvalues. Bull. London Math. Soc. , 1985 , 17 , 137–138.
https://doi.org/10.1112/blms/17.2.137

14. Zhang , F. Z. Quaternions and matrices of quaternions. Linear Algebra Appl. , 1997 , 251 , 21–57.
https://doi.org/10.1016/0024-3795(95)00543-9

 
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Current Issue: Vol. 68, Issue 1, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December