A Novel Approach to Necessary and Sufficient Conditions for the Diagonalization of Refined Neutrosophic Matrices

Olgun, Necati; Hatip, Ahmed; Bal, Mikail; Abobala, Mohammad

doi:10.54216/ijns.160202

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…In applied mathematics, it is important to compute eigen values and vectors, that is because these values can be used in statistices [ 13], and diagonalization [3 ].…”

Section: The Applications Of N-refined Ah-isometry In Matrix Computingmentioning

confidence: 99%

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On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

Katy¹,

N.N.Thjeel²,

Zahra³

et al. 2022

IJNS

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This work is dedicated to classifying the general n-refined neutrosophic ring by building a ring isomorphism and the direct product of the corresponding classical rings with itself. On the other hand, we use the classification property to solve the problem of n-refined neutrosophic computing of Eigen values and Eigen vectors of an n-refined neutrosophic matrix. Also, it will be applied to solve n-refined linear systems and models.

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“…In applied mathematics, it is important to compute eigen values and vectors, that is because these values can be used in statistices [ 13], and diagonalization [3 ].…”

Section: The Applications Of N-refined Ah-isometry In Matrix Computingmentioning

confidence: 99%

“…Neutrosophic logic as a new branch of mathematical philosophy has an impact in many fields of human knowledge. We see a lot of applications of Smarandache's work [7] in algebra, analysis, matrix computing, and geometry [1][2][3][4][5][6][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

Katy¹,

N.N.Thjeel²,

Zahra³

et al. 2022

IJNS

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“…Symbolic 2-plithogenic matrices were defined and studied in [14]; these matrices consist of symbolic 2-plithogenic real entries. These matrices are recognized as a similar structure of refined neutrosophic matrices and structures [15][16][17][18][19][20][21][22][23][24]. In matrix theory, it is very important to deal with the exponents of matrices and their related problems, such as how to diagonalize a matrix, and how to compute eigenvalues and eigenvectors.…”

Section: Introductionmentioning

confidence: 99%

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Merkepci

2023

Symmetry

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Symbolic n-plithogenic sets are considered to be modern concepts that carry within their framework both an algebraic and logical structure. The concept of symbolic n-plithogenic algebraic rings is considered to be a novel generalization of classical algebraic rings with many symmetric properties. These structures can be written as linear combinations of many symmetric elements taken from other classical algebraic structures, where the square symbolic k-plithogenic real matrices are square matrices with real symbolic k-plithogenic entries. In this research, we will find easy-to-use algorithms for calculating the determinant of a symbolic 3-plithogenic/4-plithogenic matrix, and for finding its inverse based on its classical components, and even for diagonalizing matrices of these types. On the other hand, we will present a new algorithm for calculating the eigenvalues and eigenvectors associated with matrices of these types. Also, the exponent of symbolic 3-plithogenic and 4-plithogenic real matrices will be presented, with many examples to clarify the novelty of this work.

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“…One of the most attractive concepts for mathematicians is algebraic structures due to their analog properties and close relationship with other branches of mathematics, such as geometry and matrix theory [1,2].…”

Section: Introductionmentioning

confidence: 99%

Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings

Hatip

2023

Symmetry

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Symbolic n-plithogenic algebraic structures are considered as symmetric generalizations of classical algebraic structures because they have n + 1 symmetric components. This paper is dedicated to generalizing symbolic 3-plithogenic rings by defining symbolic 4-plithogenic rings and 5-plithogenic rings; these new classes of n-symbolic plithogenic algebraic structures will be defined for the first time, and their algebraic substructures will be studied. AH structures are considered to be a sign of the presence of symmetry within these types of ring, as they consist of several parts that are similar in structure and symmetrical, and when combined with each other, they have a broader structure resembling the classical consonant structure. Many related substructures will be presented such as 4-plithogenic/5-plithogenic AH-ideals, 4-plithogenic/5-plithogenic AH-homomorphisms, and 4-plithogenic AHS-isomorphisms will be discussed. We will show our results in terms of theorems, with many clear numerical examples that explain the novelty of this work.

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A Novel Approach to Necessary and Sufficient Conditions for the Diagonalization of Refined Neutrosophic Matrices

Cited by 5 publications

References 3 publications

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices

Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings

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