## Figures and Topics from this paper

## 102 Citations

Dual Quaternion Involutions and Anti-Involutions

- Mathematics
- 2013

An involution or anti-involution is a self-inverse linear mapping. In this paper, we present involutions and anti-involutions of dual quaternions. In order to do this, quaternion conjugate, dual…

Involutions of Complexified Quaternions and Split Quaternions

- Mathematics
- 2013

An involution or anti-involution is a self-inverse linear mapping. Involutions and anti-involutions of real quaternions were studied by Ell and Sangwine [15]. In this paper we present involutions and…

Involution Matrices of Real Quaternions

- Mathematics
- 2016

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding…

Involutions in Dual Split-Quaternions

- Mathematics
- 2016

Involutions and anti-involutions are self-inverse linear mappings. In three-dimensional Euclidean space $${\mathbb{R}^{3}}$$R3, a reflection of a vector in a plane can be represented by an involution…

A new eigenspace characterization of split-quaternion involutions

- Mathematics
- 2021

It is well known that a general quaternion algebra over a field F of characteristic different from 2 is either a division algebra or is split, which means isomorphic to the algebra of -matrices with…

Kinematics of Dual Quaternion Involution Matrices

- Mathematics
- 2016

Abstract: Rigid-body (screw) motions in three-dimensional Euclidean space R^3 can be represented by involution (resp. anti-involution) mappings obtained by dual-quaternions which are self-inverse and…

Characterizations of automorphic and anti-automorphic involutions of the quaternions

- Mathematics
- 2020

ABSTRACT In this paper we give two characterizations of those involutions on the algebra of quaternions that are automorphisms or anti-automorphisms, one in terms of inner automorphisms and the other…

On k-conjugate of Quaternions

- Mathematics
- 2017

In this paper, we investigate some special involutions of the quaternions these are functions of a quaternion variable that are self-inverse. We consider the conjugate of quaternion matrices by the…

Consimilarity of quaternions and coneigenvalues of quaternion matrices

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2015

Biquaternion (Complexified Quaternion) Roots of −1

- Mathematics
- 2005

Abstract.The roots of −1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are derived. There are trivial solutions (the…

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