基于Cayley-Dickson构造的二阶实矩阵幂的计算方法  

A Method for Calculating the Power of 2-Order Real Matrix Based on Cayley-Dickson Construction

作　　者：邓勇 DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844000,Xinjiang,China;Research Center of Modern Mathematics and Its Application,Kashi University,Kashi 844000,Xinjiang,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000 [2]喀什大学现代数学及其应用研究中心,新疆喀什844000

出　　处：《喀什大学学报》2024年第3期12-16,共5页Journal of Kashi University

基　　金：国家自然科学基金项目(12061039)。

摘　　要：提出了一种基于Cayley-Dickson构造的二阶实矩阵方幂的计算方法 .该方法利用Cayley-Dickson构造,将二阶实矩阵转化为四个实数和span{σ_(0),σ_(1),σ_(2),σ_(3)}中四个实2阶基矩阵σ_(0),σ_(1),σ_(2),σ_(3)的乘积之和,并利用这四个实数构成的4维向量的递推公式来计算二阶实矩阵的幂.通过MATLAB程序的验证,结果表明,该方法具有较高的计算效率,有效地解决了二阶实矩阵方幂的精确计算问题.A method for calculating the power of the 2-order real matrix based on the Cayley-Dickson construction is proposed.This method uses the Cayley-Dickson structure to transform the 2-order real matrix into the sum of the product of four real numbers and four real 2-order base matrixσ_(0),σ_(1),σ_(2),σ_(3) of span{σ_(0),σ_(1),σ_(2),σ_(3)},and uses the recursive formula of the 4-dimensional vector composed of these four real numbers to calculate the power of the 2-order real matrix.The experimental results of the MATLAB code show that the method has high computational efficiency and effectively solves the problem of accurate calculation of the power of the 2-order real matrix.

关 键 词：Cayley-Dickson构造 二阶实矩阵 矩阵的幂 MATLAB程序 

分 类 号：O151.21[理学—数学]