On Complex Split Quaternion Matrices

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Erdogdu M., ÖZDEMİR M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.23, no.3, pp.625-638, 2013 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 23 Issue: 3
• Publication Date: 2013
• Doi Number: 10.1007/s00006-013-0399-z
• Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.625-638
• Akdeniz University Affiliated: Yes

Abstract

In this paper, we present some important properties of complex split quaternions and their matrices. We also prove that any complex split quaternion has a 4 x 4 complex matrix representation. On the other hand, we give answers to the following two basic questions "If AB = I, is it true that BA = I for complex split quaternion matrices?" and "How can the inverse of a complex split quaternion matrix be found?". Finally, we give an explicit formula for the inverse of a complex split quaternion matrix by using complex matrices.