设α=(1,1,1)^T(转置),β=(1,0,1)^T(转置),矩阵A=αβ^T(转置),k为正整数,矩阵A的k次方

问题描述:

设α=(1,1,1)^T(转置),β=(1,0,1)^T(转置),矩阵A=αβ^T(转置),k为正整数,矩阵A的k次方

A^k = (αβ^T)^k = (αβ^T) * (αβ^T) * (αβ^T) * ...* (αβ^T) 【k个(αβ^T)连乘】= α * β^T * α * β^T * α * β^T * ...* α * β^T= α * (β^T*α) * (β^T*α) * (β^T*α) * ...* (β^T*α) * β^...