Abstract
This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.
Highlights
IntroductionDenote the sets of quaternions and split quaternions by H and Hs , respectively
A quaternion, which was found in 1840 by William Rowan Hamilton [1], is in the form of q =q1 + q2i + q3 j + q4k, i2 = j2 = k2 = −1, ijk = −1, in which q1, q2, q3, q4 ∈ R, and ij =− ji =k, jk =−kj =i, ki =−ik =j
This paper gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics
Summary
Denote the sets of quaternions and split quaternions by H and Hs , respectively In [10], the author studied the problems of eigenvalues and eigenvectors of quaternion matrices by means of complex representation and companion vector. In [12], by means of complex representation of a split quaternion matrix, the authors studied the problems of right split quaternion eigenvalues and eigenvectors of a split quaternion matrix. We study the problem of right eigenvalues and associated right eigenvectors of the v-quaternion matrix.
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