Algebraic Construction for Dual Quaternions with GCN

Abstract

In this paper, we explain how dual quaternion theory can extend to dual quaternions with generalized complex number (GCN) components. More specifically, we algebraically examine this new type dual quaternion and give several matrix representations both as a dual quaternion and as a GCN.

Keywords

• Generalized complex number
• Dual quaternion
• Matrix form

GCN Katsayılı Dual Kuaterniyonlar için Cebirsel Yapı

Abstract

Bu çalışmada, dual kuaterniyon teorisinin genelleştirilmiş kompleks sayı (GCN) katsayılı dual kuaterniyonlara nasıl genişletilebileceğini açıklıyoruz. Daha özel olarak, bu yeni tip dual kuaterniyonun cebirsel olarak incelenmesini ve çeşitli matris temsillerini hem dual kuaterniyon hem de GCN olarak veriyoruz.

Keywords

• Genelleştirilmiş kompleks sayı
• Dual kuaterniyon
• Matris form

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