カテゴリー: ジョルダン標準形

\[ \left(J_{n}^{m}\left(\lambda\right)\right)_{i,j}=C\left(m,j-i\right)\lambda^{m+i-j} \]

\[ J_{n}\left(\lambda\right)=\left(\begin{array}{cccccc} \lambda & 1 & 0 & \cdots & 0 & 0\\ 0 & \lambda & 1 & \ddots & 0 & 0\\ 0 & 0 & \lambda & \ddots & 0 & 0\\ \vdots & \vdots & \ddots & \ddots & \vdots & \vdots\\ 0 & 0 & 0 & \cdots & \lambda & 1\\ 0 & 0 & 0 & \cdots & 0 & \lambda \end{array}\right) \]

\[ \dim\ker\left(\left(\lambda_{k}I-A\right)^{n_{k}}\right)=n_{k} \]

\[ \widetilde{W}\left(\lambda_{k}\right)=\ker\left(\left(A-\lambda_{k}I\right)^{n_{k}}\right) \]