Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices
In this paper, we discuss some properties of left
spectrum and give the representation of linear preserver map the left
spectrum of diagonal quaternionic matrices.
[1] J. L. Brenner, Matrices of quaternions, PacJMath., vol. 1,1951, pp.
329-335.
[2] G. Frobenius, Ubear die darstellung der endkichen gruppen durch linear
substitutionen. S.B.Dentch. Akad. Wiss. Berlin, 1897, pp. 994-1015.
[3] A. Guterman, C. K. Li, and P. ˇSemrl. Some general techniques on linear
preserver problems. Linear Algebra Appl., vol. 315, 2000, pp.61-81.
[4] L. Huang, W. So, On left eigenvalues of a quaternionic matrix, Linear
Algebra and its Applications, vol. 323, 2001, pp. 105-116.
[5] H. C. Lee, Eigenvalues and canonical forms of matrices with quaternion
coefficients, Proc.Roy. Irish Acad., vol. 52A, 1949, pp. 253-260.
[6] W. So, Left eigenvalues of quaternionic matrices, Unpublished
manuscript, 1995.
[7] R. M. W. Wood, Quaternionic eigenvalues. Bull. Loudon Math soc.,
vol.17, 1985, pp.118-137.
[8] F. Zhang, Quaternion and Matrices of Quaternions, Linear Algebra and
It’s Application, vol. 251, 1997, pp. 21-57.
[1] J. L. Brenner, Matrices of quaternions, PacJMath., vol. 1,1951, pp.
329-335.
[2] G. Frobenius, Ubear die darstellung der endkichen gruppen durch linear
substitutionen. S.B.Dentch. Akad. Wiss. Berlin, 1897, pp. 994-1015.
[3] A. Guterman, C. K. Li, and P. ˇSemrl. Some general techniques on linear
preserver problems. Linear Algebra Appl., vol. 315, 2000, pp.61-81.
[4] L. Huang, W. So, On left eigenvalues of a quaternionic matrix, Linear
Algebra and its Applications, vol. 323, 2001, pp. 105-116.
[5] H. C. Lee, Eigenvalues and canonical forms of matrices with quaternion
coefficients, Proc.Roy. Irish Acad., vol. 52A, 1949, pp. 253-260.
[6] W. So, Left eigenvalues of quaternionic matrices, Unpublished
manuscript, 1995.
[7] R. M. W. Wood, Quaternionic eigenvalues. Bull. Loudon Math soc.,
vol.17, 1985, pp.118-137.
[8] F. Zhang, Quaternion and Matrices of Quaternions, Linear Algebra and
It’s Application, vol. 251, 1997, pp. 21-57.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:71715", author = "Geng Yuan and Yiwan Guo and Fahui Zhai and Shuhua Zhang", title = "Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices", abstract = "In this paper, we discuss some properties of left
spectrum and give the representation of linear preserver map the left
spectrum of diagonal quaternionic matrices.", keywords = "Quaternionic matrix, left spectrum, linear preserver
map.", volume = "9", number = "3", pages = "195-4", }