Linear Maps That Preserve Left Spectrum of Diagonal Quaternionic Matrices

Authors: Geng Yuan, Yiwan Guo, Fahui Zhai, Shuhua Zhang

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338582

References:

[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[6] W. So, Left eigenvalues of quaternionic matrices, Unpublished manuscript, 1995.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.