Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary sufficient solvability conditions for a system Sylvester-type quaternion matrix equations, give an expression general solution to when it is solvable. As application system, consider special symmetry solution, named η-Hermitian equations. Moreover, present algorithm numerical example verif...

Claims were made in an article by Wang and Ma in 2013 that they had devised an algorithm for the quaternion LU decomposition that was significantly faster than the LU decomposition implemented in the Quaternion Toolbox for Matlab (QTFM). These claims have been tested and found to be unsupported by Matlab code supplied to the author by Wang and Ma. The author’s tests are presented, and test code...

Nonlinear tracking control of unmanned underwater vehicles (UUVs) in 6 degrees of freedom (DOF) is discussed. The 4-parameter unit quaternion is used in a singularity-free representation of attitude. Several control laws based on a generalized Lyapunov function for the attitude dynamics are derived, including feedback from the vector quaternion, the Euler rotation vector and the Rodrigues param...

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence ?-anti-Hermitian solution to system constrained matrix equations over algebra. also obtain expression general when it is solvable. Finally, provide numerical example verify main results paper.

We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N , we ...

In this paper we propose a novel approach to measuring curvature in color or vector-valued images (up to 4-dimensions) based on quaternion singular value decomposition of a Hessian matrix. This approach generalizes the existing scalar-image curvature approach which makes use of the eigenvalues of the Hessian matrix [1]. In the case of vector-valued images, the Hessian is no longer a 2D matrix b...