On the Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations

Mohammad Abobala,Parimala Mani

doi:10.1155/2021/5591576

Abstract

The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

Highlights

Neutrosophy is a new branch of philosophy founded by Smarandache [1, 2] to deal with uncertainty in real-life problems.Neutrosophic concepts found their way in many other fields, such as classification [3, 4], number theory [5, 6], algebraic equations [7, 8], Boolean algebra [9] and optimization [10].Neutrosophic algebra began with Smarandache and Kandasamy in [11], where they defined neutrosophic rings and fields for the first time
We have proved that every neutrosophic matrix can be represented uniquely by a neutrosophic linear vector space transformation
We have showed that the linear property of any neutrosophic vector space function implies the AH-structure of this function

Summary

Introduction

Neutrosophy is a new branch of philosophy founded by Smarandache [1, 2] to deal with uncertainty in real-life problems. Neutrosophic concepts found their way in many other fields, such as classification [3, 4], number theory [5, 6], algebraic equations [7, 8], Boolean algebra [9] and optimization [10]. We prove that every linear transformation between two neutrosophic vector spaces must have an AH structure

Preliminaries

Main Discussion

Conclusion

Open Problem