Neutrosophic Quadruple Vector Spaces and Their Properties
In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations...
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/8/758 |
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| author | Vasantha Kandasamy W.B. Ilanthenral Kandasamy Florentin Smarandache |
| author_facet | Vasantha Kandasamy W.B. Ilanthenral Kandasamy Florentin Smarandache |
| author_sort | Vasantha Kandasamy W.B. |
| collection | DOAJ |
| description | In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals <i>R</i> or the field of complex numbers <i>C</i> or the finite field of characteristic <i>p</i>, <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>; <i>p</i> a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector spaces. So this problem is proposed as a conjecture in the final section. |
| first_indexed | 2024-12-19T07:44:56Z |
| format | Article |
| id | doaj.art-70880bbb229148d480461123cca7e583 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-19T07:44:56Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-70880bbb229148d480461123cca7e5832022-12-21T20:30:21ZengMDPI AGMathematics2227-73902019-08-017875810.3390/math7080758math7080758Neutrosophic Quadruple Vector Spaces and Their PropertiesVasantha Kandasamy W.B.0Ilanthenral Kandasamy1Florentin Smarandache2School of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632014, IndiaSchool of Computer Science and Engineering, Vellore Institute of Technology, Vellore 632014, IndiaDepartment of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USAIn this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals <i>R</i> or the field of complex numbers <i>C</i> or the finite field of characteristic <i>p</i>, <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>; <i>p</i> a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector spaces. So this problem is proposed as a conjecture in the final section.https://www.mdpi.com/2227-7390/7/8/758Neutrosophic Quadruple (NQ)Neutrosophic Quadruple setNQ vector spacesNQ linear algebrasNQ basisNQ vector spacesorthogonal or dual NQ vector subspaces |
| spellingShingle | Vasantha Kandasamy W.B. Ilanthenral Kandasamy Florentin Smarandache Neutrosophic Quadruple Vector Spaces and Their Properties Mathematics Neutrosophic Quadruple (NQ) Neutrosophic Quadruple set NQ vector spaces NQ linear algebras NQ basis NQ vector spaces orthogonal or dual NQ vector subspaces |
| title | Neutrosophic Quadruple Vector Spaces and Their Properties |
| title_full | Neutrosophic Quadruple Vector Spaces and Their Properties |
| title_fullStr | Neutrosophic Quadruple Vector Spaces and Their Properties |
| title_full_unstemmed | Neutrosophic Quadruple Vector Spaces and Their Properties |
| title_short | Neutrosophic Quadruple Vector Spaces and Their Properties |
| title_sort | neutrosophic quadruple vector spaces and their properties |
| topic | Neutrosophic Quadruple (NQ) Neutrosophic Quadruple set NQ vector spaces NQ linear algebras NQ basis NQ vector spaces orthogonal or dual NQ vector subspaces |
| url | https://www.mdpi.com/2227-7390/7/8/758 |
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