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Title of Journal: Adv Appl Clifford Algebras

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Abbravation: Advances in Applied Clifford Algebras

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Springer Basel

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DOI

10.1002/cne.902790212

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1661-4909

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An Efficient Method for Solving Equations in Gener

Authors: Cristina Flaut Vitalii Shpakivskyi
Publish Date: 2014/08/31
Volume: 25, Issue: 2, Pages: 337-350
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Abstract

Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems mechanics etc It is known that are two types of nonisomorphic generalized quaternion algebras namely the algebra of quaternions and the algebra of coquaternions In this paper we present the formulae to pass from a basis in the generalized quaternion algebras to a basis in the division quaternions algebra or to a basis in the coquaternions algebra and vice versa The same result was obtained for the generalized octonion algebra Moreover we emphasize the applications of these results to the algebraic equations and De Moivre’s formula in generalized quaternion algebras and in generalized octonion division algebras

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Other Papers In This Journal:
  1. Twistors in Geometric Algebra
  2. On Polynomial Solutions of Generalized Moisil-Théodoresco Systems and Hodge-de Rham Systems
  3. Geometric Algebra to Model Uncertainties in the Discretizable Molecular Distance Geometry Problem
  4. Half Dirichlet Problems and Decompositions of Poisson Kernels
  5. Differential Operators Associated to the Cauchy-Fueter Operator in Quaternion Algebra
  6. Properties of Solutions to A-Harmonic System and A-Dirac System
  7. Matrix Mechanics of the Relativistic Point Particle and String in Clifford Space
  8. Harmonic Forms on Conformal Euclidean Manifolds: The Clifford Multivector Approach
  9. Two Novel Algebraic Techniques for Quaternion Least Squares Problems in Quaternionic Quantum Mechanics
  10. Operator Identities in q -Deformed Clifford Analysis
  11. Inverse Kinematics for a 6-DOF Walking Humanoid Robot Leg
  12. (1,1)-Forms Acting on Spinors on Kähler Surfaces
  13. Multiplicative Representation of a Hyperbolic non Distributive Algebra
  14. On the Quaternionic B 2 -Slant Helices in the Euclidean Space E 4
  15. The octonions form an Azumaya algebra in certain braided linear Gr-categories
  16. On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions
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