Results 11 to 20 of about 35,019 (267)

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, 2022
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 ...
Wenxv Ding, Ying Li, Anli Wei, Zhihong Liu   +3 more
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A new method based on semi-tensor product of matrices for solving reduced biquaternion matrix equation $ \sum\limits_{p = 1}^l A_pXB_p = C $ and its application in color image restoration

Mathematical Modelling and Control, 2023
In this paper, semi-tensor product of real matrices is extended to reduced biquaternion matrices, and then some new conclusions of the reduced biquaternion matrices under the vector operator are proposed using semi-tensor product of reduced biquaternion ...
Jianhua Sun, Ying Li, Mingcui Zhang, Zhihong Liu , Anli Wei   +4 more
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H-representation method for solving reduced biquaternion matrix equation

Mathematical Modelling and Control, 2022
In this paper, we study the Hankel and Toeplitz solutions of reduced biquaternion matrix equation (1.1). Using semi-tensor product of matrices, the reduced biquaternion matrix equation (1.1) can be transformed into a general matrix equation of the form ...
Xueling Fan, Ying Li, Wenxv Ding, Jianli Zhao   +3 more
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Three special kinds of least squares solutions for the quaternion generalized Sylvester matrix equation

AIMS Mathematics, 2022
In this paper, we propose an efficient method for some special solutions of the quaternion matrix equation AXB+CYD=E. By integrating real representation of a quaternion matrix with H-representation, we investigate the minimal norm least squares solution ...
Anli Wei, Ying Li, Wenxv Ding, Jianli Zhao   +3 more
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Perfect hypercomplex algebras: Semi-tensor product approach

Mathematical Modelling and Control, 2021
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebras (PHAs) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product (STP) of matrices are reviewed.
Daizhan Cheng, Zhengping Ji , Jun-e Feng, Shihua Fu, Jianli Zhao   +4 more
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Resolution of Fuzzy Relational Inequalities with Boolean Semi-Tensor Product Composition

Mathematics, 2021
Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition.
Shuling Wang, Haitao Li
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Trajectory tracking approach to logical (control) networks

AIMS Mathematics, 2022
Vector form expression of logical (control) networks is presented. From this aspect, the trajectory table is proposed to investigate Boolean networks. Based on it, the topology structure, controllability and observability of logical (control) networks ...
Xiaoyu Zhao, Shihua Fu
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Frame-indifference of cross products, rotations, and the permutation tensor

Theoretical and Applied Mechanics Letters, 2020
: Under improper transformations, the traditional transformation laws for cross products, the permutation tensor, and rotations are incorrect. For a cross product, using a counter-example the left-hand rule is proved wrong.
Maolin Du
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Solvability of the Sylvester equation AX−XB=C under left semi-tensor product

Mathematical Modelling and Control, 2022
This paper investigates the solvability of the Sylvester matrix equation AX−XB=C with respect to left semi-tensor product. Firstly, we discuss the matrix-vector equation AX−XB=C under semi-tensor product.
Naiwen Wang
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Tensor product dual frames

Journal of Inequalities and Applications, 2019
To construct dual frames with good structure for a given frame is a fundamental problem in the theory of frames. The tensor product duals of tensor product frames can provide a rank-one decomposition of bounded antilinear operators between two Hilbert ...
Ya-Hui Wang, Yun-Zhang Li
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