An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications. (1st September 2014)

• Record Type: Journal Article
• Authors: Jiang, Tongsong; Cheng, Xuehan; Ling, Sitao
• Other Names: Min Fan Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2014(2014)
• Publication Date: 2014-09-01
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2014/795203
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices. It sets up an algebraic bridge between consimilarity and similarity, and turns the theory of consimilarity of quaternion matrices into that of ordinary similarity of complex matrices. This paper also gives algebraic methods for finding coneigenvalues and coneigenvectors of quaternion matrices by means of complex representation of a quaternion matrix.