Question
Show that if $J=\operatorname{diag}\left\{C_{\lambda_1}^{(5)}, C_{\lambda_2}^{(3)}, C_{\lambda_3}^{(2)}\right\}$, then $\left(J-\lambda_1 I_{10}\right)^5\left(J-\lambda_2 I_{10}\right)^3\left(J-\lambda_3 I_{10}\right)^2=O$.
Step 1
The matrix $J$ is a block diagonal matrix with Jordan blocks corresponding to eigenvalues $\lambda_1$, $\lambda_2$, and $\lambda_3$. The sizes of these blocks are $5$, $3$, and $2$ respectively. Thus, $J$ can be written as: \[ J = Show more…
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