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Book_4_《矩阵力量》 | 鸢尾花书:从加减乘除到机器学习;上架!
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Ch13_p12_Eq.(26) 少了n-1次幂 #149

Closed shuoChenTHU closed 2 months ago

shuoChenTHU commented 3 months ago

第二项需要把n-1次幂补充上吧

$$ \boldsymbol{A}^n=\boldsymbol{V} \boldsymbol{D} \boldsymbol{V}^{-1} \left( \boldsymbol{V} \boldsymbol{D} \boldsymbol{V}^{-1} \right)^{n-1} $$

然后中间的 $\boldsymbol{V}^{-1} \boldsymbol{V}$ 显然都会消掉,就可以得到

$$ \boldsymbol{A}^n=\boldsymbol{V} \boldsymbol{D} \boldsymbol{V}^{-1} \left( \boldsymbol{V} \boldsymbol{D} \boldsymbol{V}^{-1} \right)^{n-1} = \boldsymbol{V} \boldsymbol{D}^n \boldsymbol{V}^{-1} $$

grafik

Visualize-ML commented 2 months ago

纸质书已经修改。