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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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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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A note on quaternion matrices and split quaternion matrix pencils
Journal of Applied Mathematics and Computing, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Journal of Okayama University, 1997
If \(H^{m\times n}\) denotes the set of all \(m\times n\) matrices over the quaternion field \( H\), a matrix \(A,A\in H^{m\times n},\) is \text{Re}-nonnegative definite if \(\text{Re}\to(X^{\ast }AX)\geqslant 0\) holds for every \(X\in H^{m\times 1}\), where \(X^{\ast }\)\ denotes the conjugate transpose of \(X\). The author finds the set of all \text{
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If \(H^{m\times n}\) denotes the set of all \(m\times n\) matrices over the quaternion field \( H\), a matrix \(A,A\in H^{m\times n},\) is \text{Re}-nonnegative definite if \(\text{Re}\to(X^{\ast }AX)\geqslant 0\) holds for every \(X\in H^{m\times 1}\), where \(X^{\ast }\)\ denotes the conjugate transpose of \(X\). The author finds the set of all \text{
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L-structured quaternion matrices and quaternion linear matrix equations
Linear and Multilinear Algebra, 2015This paper focuses on L-structured quaternion matrices. L-structured real matrices, conditions for the existence of solutions and the general solution of linear matrix equations were studied in the paper [Magnus JR. L-structured matrices and linear matrix equations, Linear Multilinear Algebra 1983;14:67–88].
Shi-Fang Yuan, Qing-Wen Wang
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