scholarly journals Matrices over hyperbolic split quaternions

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 913-920 ◽  
Author(s):  
Melek Erdoğdu ◽  
Mustafa Özdemir
Keyword(s):  
Matrix Representation ◽  
Quaternion Matrix ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Quaternion Matrices ◽  
Hyperbolic Split Quaternion ◽  
Split Quaternion Matrix

In this paper, we present some important properties of matrices over hyperbolic split quaternions. We examine hyperbolic split quaternion matrices by their split quaternion matrix representation.

scholarly journals On the Consimilarity of Split Quaternions and Split Quaternion Matrices

2016 ◽  
Vol 24 (3) ◽  
pp. 189-207 ◽  
Author(s):  
Hidayet Hüda Kösal ◽  
Mahmut Akyiğit ◽  
Murat Tosun
Keyword(s):  
Split Quaternion ◽  
Solvability Conditions ◽  
Split Quaternions ◽  
General Solutions ◽  
Quaternion Matrices

AbstractIn 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 equationsandin split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.

Cramer’s rule over quaternions and split quaternions: A unified algebraic approach in quaternionic and split quaternionic mechanics

2020 ◽  
pp. 2150080
Author(s):  
Gang Wang ◽  
Dong Zhang ◽  
Zhenwei Guo ◽  
Tongsong Jiang
Keyword(s):  
Matrix Representation ◽  
Linear Equations ◽  
Algebraic Approach ◽  
Complex Matrix ◽  
Split Quaternions ◽  
Quaternion Matrices ◽  
Cramer’S Rule ◽  
Algebraic Technique

This paper aims to present, in a unified manner, Cramer’s rule which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies Cramer’s rule for the system of v-quaternionic linear equations by means of a complex matrix representation of v-quaternion matrices, and gives an algebraic technique for solving the system of v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for Cramer’s rule in quaternionic and split quaternionic mechanics.

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