已知矩阵C=(1 2 3),B=(1 1/2 1/3),又A=B^T(B的转置矩阵)*C,求A^n

已知矩阵C=(1 2 3),B=(1 1/2 1/3),又A=B^T(B的转置矩阵)*C,求A^n
已知矩阵C=(1 2 3),B=(1 1/2 1/3),又A=B^T(B的转置矩阵)*C,求A^n

已知矩阵C=(1 2 3),B=(1 1/2 1/3),又A=B^T(B的转置矩阵)*C,求A^n
CB' = 1*1+2*(1/2)+3*(1/3) = 3.
所以
A^n = (B'C)(B'C)...(B'C) (n个连乘)
= B'(CB')(CB')...(CB')C (乘法结合侓)
= 3^(n-1) B'C
=
3^(n-1) 2*3^(n-1) 3^n
3^(n-1)/2 3^(n-1) 3^n/2
3^(n-2) 2*3^(n-2) 3^(n-1)
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