Abstract
Involutions and anti-involutions are self-inverse linear mappings. In three-dimensional Euclidean space \({\mathbb{R}^{3}}\), a reflection of a vector in a plane can be represented by an involution or anti-involution mapping obtained by real-quaternions. A reflection of a line about a line in \({\mathbb{R}^{3}}\) can also be represented by an involution or anti-involution mapping obtained by dual real-quaternions. In this paper, we will represent involution and anti-involution mappings obtaind by dual split-quaternions and a geometric interpretation of each as rigid-body (screw) motion in three-dimensional Lorentzian space \({\mathbb{R}_1^{3} }\).
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