Foundational aspects of a new matrix holomorphic structure
Purpose – In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis. Design/methodology/approach – We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+i...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Emerald Publishing
2025-01-01
|
| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2023-0002/full/pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Purpose – In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis. Design/methodology/approach – We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4. Findings – We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties. Originality/value – We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable. |
|---|---|
| ISSN: | 1319-5166 2588-9214 |