In this study, we present higher order Jacobsthal numbers. Then define quaternions by using We give the concept of norm and conjugate for these quaternions. express prove some propositions related to Also, find recurrence relation, Binet formula generating function Finally, calculate Cassini, Catalan, Vajda d’Ocagne identities

The classical matrix groups are of fundamental importance in many parts of geometry and algebra. Some of them, like Sp.n/, are most conceptually defined as groups of quaternionic matrices. But, the quaternions not being commutative, we must reconsider some aspects of linear algebra. In particular, it is not clear how to define the determinant of a quaternionic matrix. Over the years, many peopl...

The four-component rotational operators called quaternions, which represent eye rotations in terms of their axes and angles, have several advantages over other representations of eye position (such as Fick coordinates): they provide easy computations, symmetry, a simple form for Listing's law, and useful three-dimensional plots of eye movements. In this paper we present algorithms for computing...

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearance of the amino acids along the evolution as inferred from work th...

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...

In a previous paper we investigated Givens transformations applied to quaternion valued matrices. Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. We show that the Fast Givens transformation, known for the real case, can also be defined for quaternion valued matrices, and we apply this technique to the r...