New Formula for Computing Quaternion Powers  

作　　者：W. Eltayeb Ahmed W. Eltayeb Ahmed(Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia;Department of Basics and Engineering Sciences, Faculty of Engineering, University of Khartoum, Khartoum, Sudan)

机构地区：[1]Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia [2]Department of Basics and Engineering Sciences, Faculty of Engineering, University of Khartoum, Khartoum, Sudan

出　　处：《Applied Mathematics》2022年第3期282-294,共13页应用数学（英文）

摘　　要：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.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.

关 键 词：QUATERNIONS Matrix Algebra Kayley-Dickson Construction 

分 类 号：O151.21[理学—数学]