Results 21 to 30 of about 77,287 (351)
RSVD for Three Quaternion Tensors with Applications in Color Video Watermark Processing
Axioms, 2023 In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of ...
Wen-Juan Chen, Shao-Wen Yu
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Quaternion to Euler angles conversion: A direct, general and computationally efficient method
PLoS ONE, 2022 Current methods of the conversion between a rotation quaternion and Euler angles are either a complicated set of multiple sequence-specific implementations, or a complicated method relying on multiple matrix multiplications.
Evandro Bernardes, S. Viollet
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Dual quaternions and dual quaternionic curves [PDF]
Filomat, 2019 After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and nonisotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual
Dagdeviren, Ali, Yuce, Salim
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Three Symmetrical Systems of Coupled Sylvester-like Quaternion Matrix Equations
Symmetry, 2022 The current study investigates the solvability conditions and the general solution of three symmetrical systems of coupled Sylvester-like quaternion matrix equations.
M. S. Mehany, Qing‐Wen Wang
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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 +3 more
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Foundations of the Quaternion Quantum Mechanics
Entropy, 2020 We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic ...
Marek Danielewski, L. Sapa
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Quaternion Filtering Based on Quaternion Involutions and its Application in Signal Processing
IEEE Access, 2019 The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized HR calculus, the quaternion ...
Gang Wang, Rui Xue
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The least squares Bisymmetric solution of quaternion matrix equation AXB=C
AIMS Mathematics, 2021 In this paper, the idea of partitioning is used to solve quaternion least squares problem, we divide the quaternion Bisymmetric matrix into four blocks and study the relationship between the block matrices. Applying this relation, the real representation
Dong Wang, Ying Li, Wenxv Ding
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Machines, 2022 This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function ...
Kazuhiko Takahashi +2 more
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On quaternionic functional analysis [PDF]
, 2006 In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the ...
Agrawal +17 more
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