A Method for Calculating the Power of 2-Order Real Matrix Based on Cayley-Dickson Construction
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.
Cayley-Dickson construction2-order real matrixpower of a matrixMATLAB code