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Journal articles on the topic 'Semi-real quaternion'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Deng, Yong, and Jiangang Tang. "The non-de moivre formula for calculating the power of 3-parameter generalized quaternions." Journal of Physics: Conference Series 2905, no. 1 (2024): 012027. https://doi.org/10.1088/1742-6596/2905/1/012027.

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Abstract In this article, a recursive formula is obtained by using the simplified substitution of the 3-parameter generalized quaternion left matrix representation. Based on it, the direct formula of nth power calculation including real quaternions, split quaternions, split semi-quaternions, and 1/4-quaternions, is derived, which is more universal to solve the problem of inconvenient calculation with the De Moivres formula when the power n is large. Finally, the correctness of the obtained results is verified by two examples.

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2

Ma, Ai-qun, Lin Chen, and Zijie Qin. "Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras." AIMS Mathematics 8, no. 3 (2022): 6026–35. http://dx.doi.org/10.3934/math.2023304.

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<abstract><p>In this paper, we investigate Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras over the field of real numbers. We prove that every Jordan semi-triple derivation on generalized quaternion algebras over the field of real numbers is a derivation. Also, we show that every left (resp, right) Jordan centralizer on generalized quaternion algebras over the field of real numbers is a left (resp, right) centralizer.</p></abstract>

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3

Fan, Xueling, Ying Li, Zhihong Liu, and Jianli Zhao. "Solving Quaternion Linear System Based on Semi-Tensor Product of Quaternion Matrices." Symmetry 14, no. 7 (2022): 1359. http://dx.doi.org/10.3390/sym14071359.

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In this paper, we use semi-tensor product of quaternion matrices, L-representation of quaternion matrices, and GH-representation of special quaternion matrices such as quaternion (anti)-centrosymmetric matrices to solve the special solutions of quaternion matrix equation. Based on semi-tensor product of quaternion matrices and the structure matrix of the multiplication of quaternion, we propose the vector representation operation conclusion of quaternion matrices, and study the different matrix representations of quaternion matrices. Then the problem of the quaternion matrix equation is transf

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4

Liu, Zhihong, Ying Li, Xueling Fan, and Wenxv Ding. "A New Method of Solving Special Solutions of Quaternion Generalized Lyapunov Matrix Equation." Symmetry 14, no. 6 (2022): 1120. http://dx.doi.org/10.3390/sym14061120.

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In this paper, we study the bisymmetric and skew bisymmetric solutions of quaternion generalized Lyapunov equation. With the help of semi-tensor product of matrices, some new conclusions on the expansion rules of row and column of matrix product on quaternion matrices are proposed and applied to the calculation of quaternion matrix equation. Using the H-representation method, the independent elements are extracted according to the structural characteristics of bisymmetric matrix and skew bisymmetric matrix, so as to simplify the operation process. Finally, it is compared with the real vector r

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5

Ding, Wenxv, Ying Li, Anli Wei, and Zhihong Liu. "Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices." AIMS Mathematics 7, no. 3 (2022): 3258–76. http://dx.doi.org/10.3934/math.2022181.

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<abstract><p>In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last.</p></abstract>

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6

Yefremov, Alexander P. "Associative Hypercomplex Algebras Arise over a Basic Set of Subgeometric One-Dimensional Elements." Mathematics 13, no. 13 (2025): 2105. https://doi.org/10.3390/math13132105.

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An abstract set of one-dimensional (spinor-type) elements randomly oriented on a plane is introduced as a basic subgeometric object. Endowing the set with the binary operations of multiplication and invertible addition sequentially yields a specific semi-group (for which an original Cayley table is given) and a generic algebraic system which is shown to generate, apart from algebras of real and complex numbers, the associative hypercomplex algebras of dual numbers, split-complex numbers, and quaternions. The units of all these algebras turn out to be composed of basic 1D elements, thus ensurin

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7

Alagöz, Yasemin, and Gözde Özyurt. "Linear Equations Systems of Real and Complex Semi-Quaternions." Iranian Journal of Science and Technology, Transactions A: Science 44, no. 5 (2020): 1483–93. http://dx.doi.org/10.1007/s40995-020-00956-7.

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8

Bossly, Rawan, Majid Ali Choudhary, Mohd Danish Siddiqi, Oḡuzhan Bahadır, and Mehmet Gülbahar. "DDVV Inequality on Submanifolds Coupled with a Slant Factor in Quaternionic Kaehler Manifolds." Axioms 14, no. 1 (2024): 6. https://doi.org/10.3390/axioms14010006.

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This work aims to provide generalized Wintgen inequalities for slant submanifolds embedded in quaternionic space forms, taking into consideration both semi-symmetric metric and semi-symmetric non-metric connections. Moreover, we discuss the same inequality for totally real, anti-invariant, and invariant submanifolds on quaternionic space forms, endowed with both semi-symmetric metric and semi-symmetric non-metric connections. We also characterized the equality case through specific forms of shape operators of Wintgen inequalities for these classes of submanifolds in quaternionic space forms, a

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9

A. Funda; OKUYUCU, YILDIZ. "Inextensible flow of a semi-real quaternionic curve in semi-euclidean space R42." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 67, no. 1 (2018): 323–32. http://dx.doi.org/10.1501/commua1_0000000854.

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10

Şenturk, Gülsüm. "A generalized quaternionic sequence with Vietoris' number components." Filomat 37, no. 28 (2023): 9753–68. http://dx.doi.org/10.2298/fil2328753s.

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In this investigation, the aim is to determine a generalized quaternionic sequence with Vietoris' number components depending on 2-parameters ? and ?. Considering specific real values ? and ?, various types of classical quaternionic sequence with Vietoris' number components can be obtained as real, split, split-semi and so on. The fundamental algebraic structures, several classical expressions, a two and three term recurrence relations are identified, as well as Catalan-like, generating function and Binet-like formulas. Furthermore, a determinantal approach is used to generate the generalized

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11

García-Pacheco, Francisco Javier, and Pablo Piniella. "Geometry of balanced and absorbing subsets of topological modules." Journal of Algebra and Its Applications 18, no. 06 (2019): 1950119. http://dx.doi.org/10.1142/s0219498819501196.

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We define the concepts of balanced set and absorbing set in modules over topological rings, which coincide with the usual concepts when restricting to topological vector spaces. We show that in a topological module over an absolute semi-valued ring whose invertibles approach [Formula: see text], every neighborhood of [Formula: see text] is absorbing. We also introduce the concept of total closed unit neighborhood of zero (total closed unit) and prove that the only total closed unit of the quaternions [Formula: see text] is its closed unit ball [Formula: see text]. On the other hand, we also pr

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12

Burkhardt, Paula, Peter Cohen, Jonathan DeWitt, et al. "Random matrix ensembles with split limiting behavior." Random Matrices: Theory and Applications 07, no. 03 (2018): 1850006. http://dx.doi.org/10.1142/s2010326318500065.

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We introduce a new family of [Formula: see text] random real symmetric matrix ensembles, the [Formula: see text]-checkerboard matrices, whose limiting spectral measure has two components which can be determined explicitly. All but [Formula: see text] eigenvalues are in the bulk, and their behavior, appropriately normalized, converges to the semi-circle as [Formula: see text]; the remaining [Formula: see text] are tightly constrained near [Formula: see text] and their distribution converges to the [Formula: see text] hollow GOE ensemble (this is the density arising by modifying the GOE ensemble

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13

Onder, Gokmen Yildiz, and Ozkaldi Karakus Siddika. "On the Quaternionic Normal Curves in the Semi-Euclidean Space E4." August 15, 2016. https://doi.org/10.5281/zenodo.825066.

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In this paper, we define the semi-real quaternionic normal curves in four dimensional semi-Euclidean space E<sup>4</sup><sub>2</sub>. We obtain some characterizations of semi-real quaternionic normal curves in terms of their curvature functions. Moreover, we give necessary and sufficient condition for a semi-real quaternionic curve to be a semi-real quaternionic normal curves in E<sup>4</sup><sub>2</sub>.

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14

Ding, Wenxv, Ying Li, Zhihong Liu, Ruyu Tao, and Mingcui Zhang. "Algebraic method for LU decomposition in commutative quaternion based on semi‐tensor product of matrices and application to strict image authentication." Mathematical Methods in the Applied Sciences, January 24, 2024. http://dx.doi.org/10.1002/mma.9905.

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As a kind of commutative and associative four‐dimensional algebra, commutative quaternion has better applications in color image and signal processing than quaternion. Matrix decomposition is of great concern in the theoretical study and numerical calculation of commutative quaternion. Two kinds of disadvantages of commutative quaternion make the decomposition of commutative quaternion matrix extremely difficult. On one hand, commutative quaternion is not a kind of complete four dimensional division algebra because of the zero divisors. On the other hand, computing the inverse of commutative q

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15

Ding, Wenxv, Ying Li, and Dong Wang. "A Real Method for Solving Quaternion Matrix Equation $$\mathbf{X}-\mathbf{A}{\hat{\mathbf{X}}}{} \mathbf{B} = \mathbf{C}$$ Based on Semi-Tensor Product of Matrices." Advances in Applied Clifford Algebras 31, no. 5 (2021). http://dx.doi.org/10.1007/s00006-021-01180-1.

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16

Minghui, Wang. "On Positive Definite Solutions of Quaternionic Matrix Equations." International Journal of Engineering, Mathematical and Physical Sciences 3.0, no. 1 (2010). https://doi.org/10.5281/zenodo.1332150.

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The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established.

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17

Alagöz, Yasemin, and Gözde Özyurt. "Real and Hyperbolic Matrices of Split Semi Quaternions." Advances in Applied Clifford Algebras 29, no. 3 (2019). http://dx.doi.org/10.1007/s00006-019-0973-0.

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