Hybrid number matrices


ÇAKIR H., ÖZDEMİR M.

Filomat, vol.37, no.27, pp.9215-9227, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 27
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2327215c
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.9215-9227
  • Keywords: Hybrid Number Matrices, Hybrid numbers, Split Quaternions
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

The aim of this study is to investigate some properties of hybrid number matrices. Firstly, we introduce hybrid numbers with some of their properties. Then we prove that any hybrid number has a 2 × 2 complex matrix representation, and we investigate hybrid number matrices using the properties of complex matrices. Also we give answers to the following basic question “If AB =I, is it true that BA =I for hybrid number matrices?” Then we define the complex adjoint matrix and the q−determinant of hybrid number matrices and give some important properties. Finally, we give an explicit formula for the inverse of a hybrid number matrix by using complex matrices.