Abstract The quaternion is a powerful and common tool to avoid singularity in rotational dynamics three-dimensional (3D) space. Here it has been particularly used as an alternative Euler angles rotation matrix. application of the exercised quadrotor modeling control. It changes represents singularity-free attitude model. for first time (for best knowledge authors), state-dependent differential ...

Quaternion measurable processes are introduced and the Dirac equation is derived from the Langevin equation associated with a two-valued process.

This article makes use of simultaneous decomposition four quaternion matrixes to investigate some Sylvester-like matrix equation systems. We present useful necessary and sufficient conditions for the consistency system equations in terms equivalence form block matrixes. also derive general solution according partition coefficient As an application system, we practical a ϕ-Hermitian provide when...

In this study, new highly parallel algorithm of two-sided Jacobi 8-D transformation is suggested. It is oriented on VLSI-implementation of special processor array. This array is built using 8-D CORDIC algorithm for quaternion valued matrix singular value decomposition. Accuracy analysis and simulation results are added. Such array can be utilized to speed up the Jacobi method realization to com...

We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2 and 3...

Up until now we have learned that a rotation in R3 about an axis through the origin can be represented by a 3×3 orthogonal matrix with determinant 1. However, the matrix representation seems redundant because only four of its nine elements are independent. Also the geometric interpretation of such a matrix is not clear until we carry out several steps of calculation to extract the rotation axis...

Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue of antisymmetric hermitian matrix initial conditions, Brownian dynamics toward the unitary symmetry is analyzed. The dynamical correlation functions of arbitrary number ...

Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of quaternions nor avoid errors accumulated in the sense of long term time. We present symplectic geometric algorithms to deal with the quaternion kinematical differ...

In this paper, we present an isomorphism between the ring of general polynomials over a division algebra D with center F and the group ring of the free monoid with [D : F ] variables over D. Using this isomorphism, we define the characteristic polynomial of any matrix over any division algebra, i.e., a general polynomial with one variable over the algebra whose roots are precisely the left eige...