Results 221 to 230 of about 2,423 (258)
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Applied Mathematics and Computation, 2008
Maximal and minimal ranks of the quaternion matrix \(C_4 - A_4XB_4\) are studied, where \(X\) is a variable quaternion matrix subject to the quaternion equations \(A_1X = C_1\), \(XB_2 = C_2\), \(A_3XB_3 = C_3\). As a corollary necessary and sufficient conditions for solvability of a system of quaternion matrix equations are obtained. Extremal ranks of
Qing-Wen Wang, Shaowen Yu
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Maximal and minimal ranks of the quaternion matrix \(C_4 - A_4XB_4\) are studied, where \(X\) is a variable quaternion matrix subject to the quaternion equations \(A_1X = C_1\), \(XB_2 = C_2\), \(A_3XB_3 = C_3\). As a corollary necessary and sufficient conditions for solvability of a system of quaternion matrix equations are obtained. Extremal ranks of
Qing-Wen Wang, Shaowen Yu
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Pacific Journal of Optimization, 2023
Summary: Quaternion singular value decomposition (QSVD) plays a fundamental role in quaternion matrix optimization. This paper introduces a two-sided random orthogonalization decomposition named quaternion matrix UTV (QUTV) decomposition to replace the QSVD in some applications of quaternion matrix optimization. The compressed randomized QUTV (CoR-QUTV)
Xu, Renjie, Wei, Yimin
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Summary: Quaternion singular value decomposition (QSVD) plays a fundamental role in quaternion matrix optimization. This paper introduces a two-sided random orthogonalization decomposition named quaternion matrix UTV (QUTV) decomposition to replace the QSVD in some applications of quaternion matrix optimization. The compressed randomized QUTV (CoR-QUTV)
Xu, Renjie, Wei, Yimin
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Quaternion Matrix Optimization: Motivation and Analysis
Journal of Optimization Theory and Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liqun Qi 0001 +3 more
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A coupled quaternion matrix equations with applications
Journal of Applied Mathematics and Computing, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Long-Sheng Liu, Shuo Zhang
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Rotation matrix optimization with quaternion
2015 10th Asian Control Conference (ASCC), 2015This paper shows that the representation with the quaternions improves the efficiency in optimization of rotation matrix. The effects of vibration caused by oscillating objects can be suppressed if the object is fixed with the adequate attitude. In general, Euler angles are widely known as a representation of rotation matrices, however it is difficult ...
Shogo Katsuki, Noboru Sebe
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Studies in Applied Mathematics, 2020
AbstractIn this paper, we obtain some basic results of quaternion algorithms and quaternion calculus on time scales. Based on this, a Liouville formula and some related properties are derived for quaternion dynamic equations on time scales through conjugate transposed matrix algorithms.
Zhien Li +3 more
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AbstractIn this paper, we obtain some basic results of quaternion algorithms and quaternion calculus on time scales. Based on this, a Liouville formula and some related properties are derived for quaternion dynamic equations on time scales through conjugate transposed matrix algorithms.
Zhien Li +3 more
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Quaternion from Rotation Matrix
Journal of Guidance and Control, 1978A quaternion is regarded as a four-parameter representation of a coordinate transformation matrix, where the four components of the quaternion are treated on an equal basis. This leads to a unified, compact, and singularity-free approach to determining the quaternion when the matrix is given.
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Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices
Advances in Applied Clifford Algebras, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erdoğdu, Melek, Özdemir, Mustafa
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Communications in Statistics - Theory and Methods, 2010
In this article, we give the density functions of the singular quaternion normal matrix and the singular quaternion Wishart matrix. Furthermore, we also give the density functions of certain singular quaternion β-matrix and the singular quaternion F-matrix in terms of the density function of the singular quaternion Wishart matrix and hypergeometric ...
Fei Li, Yifeng Xue
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In this article, we give the density functions of the singular quaternion normal matrix and the singular quaternion Wishart matrix. Furthermore, we also give the density functions of certain singular quaternion β-matrix and the singular quaternion F-matrix in terms of the density function of the singular quaternion Wishart matrix and hypergeometric ...
Fei Li, Yifeng Xue
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A Quaternion Matrix Equation with Two Different Restrictions
Advances in Applied Clifford Algebras, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He, Zhuo-Heng, Wang, Meng
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