We present explicit formulas for the distributions of the extreme eigenvalues of the β–Jacobi random matrix ensemble in terms of the hypergeometric function of a matrix argument. For β = 1, 2, 4, these formulas specialize to the well-known real, complex, and quaternion Jacobi ensembles, respectively.

This paper considers a robust strong tracking nonlinear filtering problem in the case there are model uncertainties including the model mismatch, unknown disturbance and status mutation in the spacecraft attitude estimation system with quaternion constraint. Two multiple fading factor matrices are employed to regulate the prediction error covariance matrix, which guarantees its symmetry. The sp...

A necessary and sufficient condition is given for the quaternion matrix equations AiX + Y Bi = Ci (i = 1, 2) to have a pair of common solutions X and Y . As a consequence, the results partially answer a question posed by Y.H. Liu (Y.H. Liu, Ranks of solutions of the linear matrix equation AX + Y B = C, Comput. Math. Appl., 52 (2006), pp. 861-872).

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.

In this paper, Direction Cosine Matrix (DCM) method for attitude and orientation estimation is discussed. DCM method was chosen due to some advantages over the popular methods such as namely Euler Angle, Quaternion in light of reliability, accuracy and computational efforts. Proposed model for each method is developed for methodology comparison. It is shown that normal Kalman Filter in DCM meth...

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra a...

In this paper, we explain how dual quaternion theory can extend to quaternions with generalized complex number (GCN) components. More specifically, algebraically examine new type and give several matrix representations both as a GCN.