Involution Matrices of Real Quaternions
نویسندگان
چکیده
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 to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R.
منابع مشابه
Involution Matrices of Real Quaternions
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 to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
متن کاملA brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices
The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
متن کاملCanonical matrices of bilinear and sesquilinear forms
Canonical matrices are given for • bilinear forms over an algebraically closed or real closed field; • sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and • sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of...
متن کاملDe- Moivre’s and Euler Formulas for Matrices of Split Quaternions
In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre’ s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.
متن کاملSkinning with dual quaternions pdf
Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix blending Cordier and Magnenat-Thalmann 2005 and. Dual quaternions a generalization of regular quaternions invented. Techdocslcoterrors.pdf.Figure 1: A comparison of dual quaternion skinning with previous methods: log-matrix. Closed-form approximation, based on dual quaternions a general.Skinning with Quaternion...
متن کامل