MATRIX FORMULATION OF REAL QUATERNIONS

Abstract

Real quaternions have been expressed in terms of 4×4 matrices by means of Hamilton operators. These matrices are applied for rotations in Euclidean 4-space, and are determined also a Hamilton motions in E⁴. We study these matrices and show that the set of these matrices with the group operation of matrix multiplication is Lie group of 6-dimension.

Keywords

• De Moivre’s formula, Homothetic motion, Lie group, Rotation, Real quaternion

REEL KUATERNİYONLARIN MATRİS FORMÜLASYONU

Abstract

Reel kuaterniyonlar Hamilton operatörleri aracılığıyla 4×4 matrisler cinsinden ifade edilmiştir. Bu matrisler Öklid 4-uzayda rotasyonlar için uygulanır ve aynı zamanda E4 bir Hamilton hareketleri tespit edilir. Biz bu matrisleri inceledik ve matris çarpımı grup ile bu matrislerin kümesi 6boyutun Lie grubu olduğunu göstermektedir

Keywords

• De Moivre formülü, Homotetik hareket, Lie grubu

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