In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full r...
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In this paper, based on the Gauss transformation of a quaternion matrix, we study the full rank decomposition of a quaternion matrix, and obtain a direct algorithm and complex structure-preserving algorithm for full rank decomposition of a quaternion matrix. In addition, we expand the application of the above two full rank decomposition algorithms and give a fast algorithm to calculate the quaternion linear equations. The numerical examples show that the complex structure-preserving algorithm is more efficient. Finally, we apply the structure-preservingalgorithm of the full rank decomposition to the sparse representation classification of color images, and the classification effect is well.
Singular value decomposition plays a prominent role in the theoretical study and numerical calculation of a quaternion matrix in applied sciences. This paper, by means of a complex representation of a quaternion matri...
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Singular value decomposition plays a prominent role in the theoretical study and numerical calculation of a quaternion matrix in applied sciences. This paper, by means of a complex representation of a quaternion matrix, studies the algorithm for the singular value decomposition of a quaternion matrix, and derives a complex structure-preserving algorithm for the singular value decomposition of a quaternion matrix. This paper also gives two examples to demonstrate the effectiveness of the algorithm.
The dual quaternion matrix has important application value in brain science and multi-agent formation control. In this paper, a practical method for realizing dual quaternion QR decomposition (DQQRD) is proposed by us...
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The dual quaternion matrix has important application value in brain science and multi-agent formation control. In this paper, a practical method for realizing dual quaternion QR decomposition (DQQRD) is proposed by using a dual quaternion Householder transformation. Since the product of dual quaternions depends on the product law of quaternions, it will face complex computational problems. If DQQRD is directly performed, it will be inefficient. Therefore, in this paper, the complex representation of a dual quaternion matrix is established by using the semi-tensor product (STP) of matrices, and the complex structure-preserving algorithm of the DQQRD is proposed. In order to improve the accuracy of the decomposition, a method of column pivoting is given. Numerical experiments show that the method is effective. Finally, the DQQRD is applied to solve the dual quaternion linear equation Ax=b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ax=b$$\end{document}.
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