Regretting It to DeathThe Peugeot 5008 might have some elements that made the owner regret. In terms of suspension, it used a leaf spring suspension instead of an independent suspension, while the 508L,...
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How to calculate the diagonal matrix corresponding to the characteristic matrix假设\(n×n\)矩阵\(A\)有\(n\)个线性无关的特征向量,如果这些向量是矩阵\(S\)的列,那么\(S^{-1}AS\)是一个对角矩阵\(\Lambda\),\(A\)的特征值在\(\Lambda\)的对角线上,即\(S^{-1}AS = \Lambda=\begin{pmatrix}\lambda_1&\;&\;\\\;&\lambda_2&\;\\\;&\;&\ddots\\\;&\;&\;&\lambda_n\end{pmatrix}\)。
计算过程如下:将特征向量\(x_i\)放在\(S\)的列上,按列计算\(AS\)可得\(AS = A\begin{pmatrix}|&|&\cdots&|\\x_1&x_2&\cdots&x_n\\|&|&\cdots&|\end{pmatrix}=\begin{pmatrix}|&|&\cdots&|\\\lambda_1x_1&\lambda_2x_2&\cdots&\lambda_nx_n\\|&|&\cdots&|\end{pmatrix}\),然后将最后一个矩阵分成两个矩阵的乘积\(S\Lambda\),即\(\begin{pmatrix}\lambda_1x_1&\lambda_2x_2&\cdots&\lambda_nx_n\end{pmatrix}=\begin{pmatrix}|&|&\cdots&|\\x_1&x_2&\cdots&x_n\\|&|&\cdots&|\end{pmatrix}\begin{pmatrix}\lambda_1&\;&\;\\\;&\lambda_2&\;\\\;&\;&\ddots\\\;&\;&\;&\lambda_n\end{pmatrix}\),所以\(AS = S\Lambda\),进而\(S^{-1}AS=\Lambda\),其中\(S\)是可逆的,因为假设它的列(特征向量)是无关的。
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