A rotation matrix can be generated by a unit timelike quaternion in the three dimensional Minkowski space. In this paper, we correspond columns of this rotation matrix to Frenet vectors of a nonlightlike curve and we find a reformulation of Frenet’s formulas of nonlightlike curves in terms of the timelike quaternions in the Minkowski 3-space. Moreover, we do same things for the parallel transpo...

The quaternionic representation of ham images, treating RGB colour components as a single unit instead of as separate components, is very effective. The advantage of using quaternion arithmetic is that the perceptually richer colour images can be represented and analyzed as a single entity, improving the accuracy of pattern recognition models. The quaternionic singular value decomposition (SVD)...

This paper contains a computational analysis and comparison of various representations of a general rigid body spatial screw displacement. Point transformations and line transformations are treated separately. In the context of point transformations, only a brief summary of the known techniques (i.e., homogeneous transforms and quaternion/vector pairs) and their computational behavior is given....

A filter for estimating spacecraft attitude quaternion and gyro drift from vector measurements in the presence of white noises in the gyro error, in the drift dynamics, and in the line-of-sight measurement error is developed. The variance parameters of the white noises are unknown, and are modeled as non-anticipative second order stochastic processes. The approach taken in this work consists in...

In this paper, we propose a necessary and sufficient condition for the solvability to system of matrix equations over commutative quaternion ring, establish an expression its general solution when it is solvable. We also present algorithm finding approximate inconsistent. Finally, give example illustrate main results paper.

In this paper, a color image inpainting problem is modeled as low rank quaternion matrix optimization problem. A has smooth property inherently and all imaginary parts of the corresponding pure are nonnegative. Based on these characteristics, we introduce novel regularized model then propose factorization algorithm with convergence analysis. Numerical experiments demonstrate efficiency our prop...