On Eigenvalues of Split Quaternion Matrices

2013 ◽  
Vol 23 (3) ◽  
pp. 615-623 ◽  
Author(s):  
Melek Erdoğdu ◽  
Mustafa Özdemir
Keyword(s):  
Split Quaternion ◽  
Quaternion Matrices

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.

On Complex Split Quaternion Matrices

2013 ◽  
Vol 23 (3) ◽  
pp. 625-638 ◽  
Author(s):  
Melek Erdoğdu ◽  
Mustafa Özdemir
Keyword(s):  
Split Quaternion ◽  
Quaternion Matrices

scholarly journals Split quaternion matrices

2012 ◽  
Vol 13 (2) ◽  
pp. 223 ◽  
Author(s):  
Yasemin Alagöz ◽  
Kürşat Hakan Oral ◽  
Salim Yüce
Keyword(s):  
Split Quaternion ◽  
Quaternion Matrices

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 split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

2021 ◽  
Vol 19 (1) ◽  
pp. 583-599
Author(s):  
Beata Bajorska-Harapińska ◽  
Jakub Jan Ludew ◽  
Barbara Smoleń-Duda ◽  
Roman Wituła
Keyword(s):  
Generating Functions ◽  
Split Quaternion ◽  
Quaternion Algebras

Abstract In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras. Explicit and recurrent formulae for Split Quaternacci sequences are given, as well as generating functions. Also, matrices related to Split Quaternaccis sequences are investigated. Moreover, new identities connecting Horadam sequences with other known sequences are generated. Analogous identities for Horadam quaternions and split Horadam quaternions are proved.

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