On Hyperbolic Split Quaternions and Hyperbolic Split Quaternion Matrices

2018 ◽  
Vol 28 (5) ◽  
Author(s):  
Gözde Özyurt ◽  
Yasemin Alagöz
Keyword(s):  
Split Quaternion ◽  
Split Quaternions ◽  
Quaternion Matrices ◽  
Hyperbolic Split Quaternion

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.

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 Some Fixed Points Results of Quadratic Functions in Split Quaternions

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Young Chel Kwun ◽  
Mobeen Munir ◽  
Waqas Nazeer ◽  
Shin Min Kang
Keyword(s):  
Fixed Points ◽  
Quadratic Polynomial ◽  
Quadratic Functions ◽  
Split Quaternion ◽  
Quadratic Polynomials ◽  
Split Quaternions

We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences.

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 An Algorithm for the Factorization of Split Quaternion Polynomials

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Daniel F. Scharler ◽  
Hans-Peter Schröcker
Keyword(s):  
Hyperbolic Plane ◽  
Dual Quaternion ◽  
Real Polynomial ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Dual Quaternions ◽  
Factorization Theory ◽  
Real Polynomials ◽  
Theory Of Motion ◽  
Univariate Polynomials

AbstractWe present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we present also geometric interpretations in terms of rulings on the quadric of non-invertible split quaternions. However, suitable real polynomial multiples of split quaternion polynomials can still be factorized and we describe how to find these real polynomials. Split quaternion polynomials describe rational motions in the hyperbolic plane. Factorization with linear factors corresponds to the decomposition of the rational motion into hyperbolic rotations. Since multiplication with a real polynomial does not change the motion, this decomposition is always possible. Some of our ideas can be transferred to the factorization theory of motion polynomials. These are polynomials over the dual quaternions with real norm polynomial and they describe rational motions in Euclidean kinematics. We transfer techniques developed for split quaternions to compute new factorizations of certain dual quaternion polynomials.

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