Quaternions are well suited to describe and combine rotations in the usual 3D euclidian space. Therefore, an increasing interest has been shown especially by engineers for symbolically computing with quaternions. To give the ability to perform manipulations on symbolic expressions involving quaternions, we designed Quaterman, a Maple package and Quaternica, a Mathematica package. We present the...

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions Binet formulas for these quaternions investigating some properties among them.

As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...

We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f ,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f ,g, or by only one pure unit quaternion f , comment on their geometric meaning, and establish invers...

The practical and accurate computation of the singular value decomposition of a quaternion matrix is of importance in vector signal processing using quaternions. We present a Jacobi algorithm for computing such an SVD, and discuss its utility and accuracy. The algorithm is included in an open-source Matlab toolbox for quaternions where it serves as an accurate reference implementation.