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Ivan Kyrchei - One of the best experts on this subject based on the ideXlab platform.
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Determinantal Representations of the Quaternion Core Inverse and Its Generalizations
Advances in Applied Clifford Algebras, 2019Co-Authors: Ivan KyrcheiAbstract:In this paper, we extend notions of the core inverse, core-EP inverse, DMP inverse, and CMP inverse over the quaternion Skew Field $${\mathbb {H}}$$ H that have some features in comparison to complex matrices. We give the direct method of their computing, namely, their determinantal representations by using column and row noncommutative determinants previously introduced by the author. As the special case, we give their determinantal representations for complex matrices as well. A numerical example to illustrate the main result is given.
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The General Solution of Quaternion Matrix Equation Having -Skew-Hermicity and Its Cramer’s Rule
Mathematical Problems in Engineering, 2019Co-Authors: Abdur Rehman, Ivan Kyrchei, Muhammad Akram, Abdul ShakoorAbstract:We determine some necessary and sufficient conditions for the existence of the -Skew-Hermitian solution to the following system over the quaternion Skew Field and provide an explicit expression of its general solution. Within the framework of the theory of quaternion row-column noncommutative determinants, we derive its explicit determinantal representation formulas that are an analog of Cramer’s rule. A numerical example is also provided to establish the main result.
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determinantal representations of general and Skew hermitian solutions to the generalized sylvester type quaternion matrix equation
Abstract and Applied Analysis, 2019Co-Authors: Ivan KyrcheiAbstract:In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and Skew-Hermitian solutions to the generalized Sylvester matrix equation involving - Hermicity over the quaternion Skew Field within the framework of the theory of noncommutative column-row determinants.
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linear differential systems over the quaternion Skew Field
arXiv: Rings and Algebras, 2018Co-Authors: Ivan KyrcheiAbstract:A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row determinants recently introduced by the author. In this paper, the algebraic structure of their general solutions are established. Determinantal representations of solutions of systems with constant coefficient matrices and sources vectors are obtained in both cases when coefficient matrices are invertible and singular. In the last case, we use determinantal representations of the quaternion Drazin inverse within the framework of the theory of column-row determinants. Numerical examples to illustrate the main results are given.
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new determinantal representations of the w weighted drazin inverse over the quaternion Skew Field
arXiv: Rings and Algebras, 2015Co-Authors: Ivan KyrcheiAbstract:Within the framework of the theory of the column and row determinants, we obtain new determinantal representations of the W-weighted Drazin inverse over the quaternion Skew Field. We give determinantal representations of the W-weighted Drazin inverse by using previously introduced determinantal representations of the Drazin inverse, the Moore-Penrose inverse, and the limit representations of the W-weighted Drazin inverse in some special case.
Junqing Wang - One of the best experts on this subject based on the ideXlab platform.
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STUDY ON SOME PROPERTIES OF Skew-SYMMETRIC AND Skew-CIRCULANT MATRIX OVER Skew Field
International Research Journal of Pure Algebra, 2016Co-Authors: Wenhui Lan, Junqing WangAbstract:I n this paper, some properties of Skew-symmetric and Skew-circulant matrix were extended from general complex domain to Skew Field. The relationships between Skew-symmetric and Skew-circulant matrix and symmetric circulant matrix, symmetric and Skew-circulant matrix and Skew-circulant matrix, over Skew Field, were obtained. Meanwhile, the linear expression of Skew-symmetric and Skew-circulant matrix under fundamental Skew-circulant matrix was also obtained. In addition, over Skew Field, the sufficient condition, which could infer that one matrix was Skew-symmetric and Skew-circulant matrix and that Skew-symmetric and Skew-circulant matrices were commutative, as well as some properties of inverse matrix of Skew-symmetric and Skew-circulant matrix were acquired
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SOME PROPERTIES OF LINEAR COMBINATIONS OF TWO IDEMPOTENT MATRICES OVER Skew Field
International Research Journal of Pure Algebra, 2016Co-Authors: Wenhui Lan, Junqing WangAbstract:I n this paper, idempotent matrices over Skew Field have been researched and some properties of idempotent matrices were extended from general complex domain to Skew Field. In this paper, the following conclusions were obtained: (1) the four equivalent conditions of idempotent matrices over Skew Field;(2) the necessary and sufficient conditions which could infer that the linear combinations
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Property of Kronecker Product of Matrices over Skew Field
2011 International Conference on Control Automation and Systems Engineering (CASE), 2011Co-Authors: Yumin Feng, Junqing WangAbstract:Kronecker product not only plays an important role in research of the matrix equation, bue also there is many applications in other respects.In this paper,we give kronecker product over Skew Field and relevant property by extendeding the property of kronecker product of two matrices on general complex domin to Skew Field.
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Rank Equalities of Sum of Matrices over Skew Field
2011 International Conference on Control Automation and Systems Engineering (CASE), 2011Co-Authors: Junqing WangAbstract:Using the relations between rank of block matrices and generalized inverse of matrices, the article obtains an rank equality of sum of matrices on Skew Field, and extends the rank equality of sum of idempotent matrices in complex Field to Skew Field.
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Partition Anti-circulant Matrix on Skew Field and it's Qualities
2009Co-Authors: Junqing Wang, Li-zhen ZhangAbstract:In this paper , the concept of the partition anti-circulant matrix on Skew Field is given,and its operational properties is discussed.
Guang-jing Song - One of the best experts on this subject based on the ideXlab platform.
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Bott-Duffin inverse over the quaternion Skew Field with applications
Journal of Applied Mathematics and Computing, 2012Co-Authors: Guang-jing SongAbstract:In this paper, we show some properties of the Bott-Duffin inverses \(A_{r_{ ( L_{1} ) }}^{ ( -1 ) }\) and \(A_{l_{ ( L_{2} ) }}^{ ( -1 ) }\) over the quaternion Skew Field. In particular, we establish the determinantal representations of these generalized inverses by the theory of the column and row determinants. Moreover, we derive some Cramer rules for the unique solution to some restricted linear quaternion equations. The findings of this paper extend some known results in the literature.
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determinantal representation of the generalized inverses over the quaternion Skew Field with applications
Applied Mathematics and Computation, 2012Co-Authors: Guang-jing SongAbstract:We first present some determinantal representations of one {1,5}-inverse of a quaternion matrix within the framework of a theory of the row and column determinants. As applications, we show some new explicit expressions of generalized inverses \(A_{r_{T_{1}, S_{1}}}^{( 2)}\), \(A_{l_{T_{2},S_{2}}}^{(2)}\) and \(A_{_{( T_{1},T_{2}) , ( S_{1},S_{2}) }}^{( 2) }\) over the quaternion Skew Field. Finally, we give the representations of the unique solution to some restricted left and right systems of quaternionic linear equations. The findings of this paper extend some known results in the literature.
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Cramer rule for the unique solution of restricted matrix equations over the quaternion Skew Field
Computers & Mathematics With Applications, 2011Co-Authors: Guang-jing Song, Qing-wen Wang, Hai-xia ChangAbstract:In this paper, we establish the determinantal representations of the generalized inverses A"r"""T"""""""1""","""S"""""""1^(^2^),A"l"""T"""""""2""","""S"""""""2^(^2^) and A"""("""T"""""""1""","""T"""""""2""")""","""("""S"""""""1""","""S"""""""2""")^(^2^) over the quaternion Skew Field by the theory of the column and row determinants. In addition, we derive some generalized Cramer rules for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature.
Orgest Zaka - One of the best experts on this subject based on the ideXlab platform.
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Skew Field of trace preserving endomorphisms of translation group in affine plane
Proyecciones (antofagasta), 2020Co-Authors: Orgest Zaka, Mohanad A MohammedAbstract:We will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an affine plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of tracepreserving endomorphisms together with the actions of ’addition’ and ’composition’ (which is in the role of ’multiplication’) forms a SkewField.
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Skew-Field of Trace-Preserving Endomorphisms, of Translation Group in Affine Plane
arXiv: General Mathematics, 2020Co-Authors: Orgest ZakaAbstract:In this paper we will show how to constructed an Skew-Field with trace-preserving endomorphisms of the affine plane. Earlier in my paper, we doing a detailed description of endomorphisms algebra and trace-preserving endomorphisms algebra in an affine plane, and we have constructed an associative unitary ring for which trace-preserving endomorphisms. In this paper we formulate and prove an important Lemma, which enables us to construct a particular trace-preserving endomorphism, with the help of which we can construct the inverse trace-preserving endomorphisms of every trace-preserving endomorphism. At the end of this paper we have proven that the set of trace-preserving endomorphisms together with the actions of 'addition' and 'composition' (which is in the role of 'multiplication') forms a Skew-Field.
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Ordered Line and Skew-Fields in the Desargues Affine Plane
arXiv: History and Overview, 2019Co-Authors: Orgest Zaka, James F. PetersAbstract:This paper introduces ordered Skew Fields that result from the construction of a Skew Field over an ordered line in a Desargues affine plane. A special case of a finite ordered Skew Field in the construction of a Skew Field over an ordered line in a Desargues affine plane in Euclidean space, is also considered. Two main results are given in this paper: (1) every Skew Field constructed over a Skew Field over an ordered line in a Desargues affine plane is an ordered Skew Field and (2) every finite Skew Field constructed over a Skew Field over an ordered line in a Desargues affine plane in $\mathbb{R}^2$ is a finite ordered Skew Field.
Wang Junqing - One of the best experts on this subject based on the ideXlab platform.
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APPLICATIONS OF COPRIME POLYNOMIALS TO THE EQUATIONS OF RANKS OF MATRIXES OVER Skew Field
International Research Journal of Pure Algebra, 2015Co-Authors: Song Zhenzhen, Wang JunqingAbstract:I n this paper, we use the relatively prime polynomial of rank identities of the product of matrix, and the method of constructing block matrix, and conducting elementary transformation, if we can add some constraints and transform the rank identities from the domain to the Skew Field, finally we get a series of the conclusion of the rank of matrices over Skew Field.
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• The Algorithm for Inverse Matrices of Symmetric r-Circulant Matrices over Skew Field
International Research Journal of Pure Algebra, 2015Co-Authors: Song Zhenzhen, Wang JunqingAbstract:T his paper mainly introduces elementary column transformation method of inverse matrix of symmetric r-circulant matrix over Skew Field by using the elementary column transformation of polynomial matrix.
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PROPERTY OF HADAMARD PRODUCT OF MATRICES OVER Skew Field
International Research Journal of Pure Algebra, 2013Co-Authors: Fan Xin, Wang JunqingAbstract:In this paper, we give product over Skew Field and relevant property by extending the property of product of two matrices on complex domain to Skew Field. Especially, this paper using the method of block matrices gets a few products’ preference ordering Inequalities about Positive Semi-definite matrices inverse.
