In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved. Moreover, we give a set of invertible elements in split quaternion algebras and in split octonion algebras.

We develop a non-compact version of the Hopf maps based on the split-algebras. The split-algebras consist of three species: split-complex numbers, split-quaternions, and split-octonions. They correspond to three non-compact Hopf maps that represent topological mapping between higher dimensional hyperboloids in different dimensions with hyperboloid-bundles. We realize such non-compact Hopf maps ...

This paper proposes a nonlinear adaptive position and attitude tracking controller for satellite proximity operations between a target and a chaser satellite. The controller requires no information about the mass and inertia matrix of the chaser satellite, and takes into account the gravitational acceleration, the gravity-gradient torque, the perturbing acceleration due to Earth’s oblateness, a...

In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative negative subscripts. line purpose, construct some new properties such as; special determinant equalities, recurrence relations, matrix formulas, Binet-like generating functions, exponential summation binomial for these quaternions.

As we know, quaternions are very efficient for representing rotations with clear geometric meaning (rotation axis and angle) and only one redundancy. Unfortunately, they do not handle translations, which meanwhile can be made multiplicative along with rotations via the use of homogeneous coordinates. Despite also being 4-tuples, homogeneous coordinates are algebraically incompatible with quater...

Recently the general orthogonal planes split with respect to any two pure unit quaternions f, g ∈ H, f = g = −1, including the case f = g, has proved extremely useful for the construction and geometric interpretation of general classes of double-kernel quaternion Fourier transformations (QFT) [7]. Applications include color image processing, where the orthogonal planes split with f = g = the gr...