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
邓勇1
作者信息
- 1. 喀什大学 数学与统计学院,新疆喀什 844000;喀什大学 现代数学及其应用研究中心,新疆喀什 844000
- 折叠
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{σ0,σ1,σ2,σ3}中四个实2阶基矩阵σ0,σ1,σ2,σ3 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.
Abstract
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 matrix σ0,σ1,σ2,σ3 of span{σ0,σ1,σ2,σ3},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Key words
Cayley-Dickson construction/2-order real matrix/power of a matrix/MATLAB code引用本文复制引用
出版年
2024
NETL
NSTL
万方数据