TITLE:
New Formula for Computing Quaternion Powers
AUTHORS:
W. Eltayeb Ahmed
KEYWORDS:
Quaternions, Matrix Algebra, Kayley-Dickson Construction
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.3,
March
31,
2022
ABSTRACT: In this work, we create a new mathematical formula that computes the power of a quaternion number raised to a positive integer by reducing the real matrix of order 4 × 4 that we take to represent this quaternion number to a matrix that makes the process of multiplying this quaternion number by itself simpler. We also present a new method for computing the power of a real matrix of order 2 × 2 as an application of this formula.