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...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2025-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2023-0002/full/pdf |
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| author | Hedi Khedhiri Taher Mkademi |
| author_facet | Hedi Khedhiri Taher Mkademi |
| author_sort | Hedi Khedhiri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ebdbb6dc8a584a789ebd66fe1a544961 |
| institution | Kabale University |
| issn | 1319-5166 2588-9214 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj-art-ebdbb6dc8a584a789ebd66fe1a5449612025-01-24T04:22:17ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142025-01-013119611710.1108/AJMS-08-2023-0002Foundational aspects of a new matrix holomorphic structureHedi Khedhiri0Taher Mkademi1Department of Mathematics, IPEIM, University of Monastir, Monastir, TunisiaDepartment of Mathematics, IPEIM, University of Monastir, Monastir, TunisiaPurpose – 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.https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2023-0002/full/pdfComplex quaternionComplex quaternionic spaceQuaternionic holomorphic functionCauchy–Riemann equations |
| spellingShingle | Hedi Khedhiri Taher Mkademi Foundational aspects of a new matrix holomorphic structure Arab Journal of Mathematical Sciences Complex quaternion Complex quaternionic space Quaternionic holomorphic function Cauchy–Riemann equations |
| title | Foundational aspects of a new matrix holomorphic structure |
| title_full | Foundational aspects of a new matrix holomorphic structure |
| title_fullStr | Foundational aspects of a new matrix holomorphic structure |
| title_full_unstemmed | Foundational aspects of a new matrix holomorphic structure |
| title_short | Foundational aspects of a new matrix holomorphic structure |
| title_sort | foundational aspects of a new matrix holomorphic structure |
| topic | Complex quaternion Complex quaternionic space Quaternionic holomorphic function Cauchy–Riemann equations |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-08-2023-0002/full/pdf |
| work_keys_str_mv | AT hedikhedhiri foundationalaspectsofanewmatrixholomorphicstructure AT tahermkademi foundationalaspectsofanewmatrixholomorphicstructure |