scholarly journals The Moore-Penrose inverses of split quaternions

2020 ◽  
pp. 1-17
Author(s):  
Wensheng Cao ◽  
Zhenhu Chang
Keyword(s):  
Split Quaternions

The geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space

2016 ◽  
Vol 13 (10) ◽  
pp. 1650116 ◽  
Author(s):  
Derya Kahvecí ◽  
Yusuf Yayli ◽  
Ísmaíl Gök
Keyword(s):  
Rotation Angle ◽  
Rotation Axis ◽  
Symmetric Matrix ◽  
Unit Length ◽  
Exponential Map ◽  
Spatial Displacement ◽  
Split Quaternions ◽  
Rodrigues Formula ◽  
Lightlike Axis ◽  
The Given

The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in [Formula: see text] and angle, the spatial displacement is represented by a [Formula: see text] semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues formula is expressed via split quaternions in Minkowski 3-space.

On the Semisimilarity and Consemisimilarity of Split Quaternions

2015 ◽  
Vol 26 (2) ◽  
pp. 847-859 ◽  
Author(s):  
Onder Gokmen Yildiz ◽  
Hidayet Huda Kosal ◽  
Murat Tosun
Keyword(s):  
Split Quaternions

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.

Multiplicative properties of integer valued polynomials over split-quaternions

2020 ◽  
pp. 1-14
Author(s):  
Antonio Cigliola ◽  
Dario Spirito ◽  
Francesca Tartarone
Keyword(s):  
Split Quaternions
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