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 this paper, we investigate a system of twelve quaternion matrix equations. Using the real representation matrix, first derive least-squares solution with least norm to system. Meanwhile, establish solvability conditions and an expression general when it is consistent.

In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an underlying noncommutative dynamics. In quaternionic quantum mechanics, the Dirac transition amplitudes 〈ψ|φ〉 are quaternion valued, that is, they have the for...

Quaternion is a four-dimensional and an extension of the complex number system. It often viewed from various fields, such as analysis, algebra, geometry. Several applications quaternions are related to object’s rotation motion in three-dimensional space form differential equation. In this paper, we do systematic literature review on development quaternion equations. We utilize PRISMA (preferred...

In [1], Savage described a unified mathematical framework for strapdown inertial navigation algorithm design. The commenting note [2] showed that the " velocity translation vector " (VTV) in the Savage's framework is equivalent to the dual part of an appropriate screw vector in the dual quaternion representation [3] and significantly simplified the VTV rate equation by way of the screw vector r...

This work is focused on impedance control of robot manipulators performing six-degree-of-freedom interaction tasks. An energy-based formulation leads to formally deriving the dynamic equation characterizing a mechanical impedance at the end effector. An inverse dynamics strategy with contact force and moment measurement is adopted to obtain a configurationindependent desired impedance. For give...

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green, and blue channels of images. A low-rank approximation for obtained by using the singular value decomposition. However, this is not optimal sense that resulting may quaternion, i.e., contains real component which useful representa...

Three-dimensional coordinate transformation problem is the most frequent problem in photogrammetry, geodesy, mapping, geographical information science (GIS), and computer vision. To overcome the drawback that traditional solution of the problem based on rotation angles depends strongly on initial value of parameter, which makes the method ineffective in the case of super-large rotation angle, t...

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared for its importance with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.-Clerk Maxwell, 1869. Quaternions came from Hamil...