New insight into quaternions and their matrices

Abstract

This paper aims to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. An alternative approach for a generalized quaternion matrix with elliptic number entries has been developed as a crucial part.

Keywords

• Generalized quaternion
• generalized complex number
• matrix representation
• elliptic number.

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