Consimilarity of quaternions and coneigenvalues of quaternion matrices

Si-Tao Ling, Xue-Han Cheng and Tong-Song Jiang

Applied Mathematics and Computation, 2015, vol. 270, issue C, 984-992

Abstract: First of all, by characterizing solutions of the quaternion equation ax=x˜b, this paper studies consimilarity of quaternions and some related consequences. For the important role of coneigenvalues in consimilarity tranformations of quaternion matrices, this paper further derives the relations between principle right coneigenvalues of a quaternion matrix and eigenvalues of the corresponding real representation matrix. Then, based on the real representation matrix, an effective algorithm is presented to calculate all coneigenvalues and the associated coneigenvectors of a quaternion matrix. Finally, two numerical examples are given to verify the effectiveness of the proposed algorithm.

Keywords: Consimilarity; Coneigenvalue; Coneigenvector; Quaternion matrix; Real representation (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:984-992

DOI: 10.1016/j.amc.2015.08.093

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