On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Author:

Kösal Hidayet Hüda1,Akyiğit Mahmut1,Tosun Murat1

Affiliation:

1. Department of Mathematics, Sakarya University, 54187 Serdivan / Sakarya / Turkey

Abstract

Abstract In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In his regard, we examine the solvability conditions and general solutions of the equations and in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.

Publisher

Walter de Gruyter GmbH

Reference20 articles.

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3. [3] J. H. Bevis, F. J. Hall and R. E. Hartwig,, The matrix equation [xxx] = C and its special cases., SIAM J. Matrix Anal. Appl. 9 (1988), 348-359.10.1137/0609029

4. [4] J. H. Bevis, F. J. Hall and R. E. Hartwig, Consimilarity and the matrix equation [xxx] = C, Current Trends in Matrix Theory. Elsevier Science Publishing Co. Inc., 1987.

5. [5] J. Cockle, On systems of algebra involving more than one imaginary, Phil. Mag. 35 (1849), 434-635.

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