Chapter 7 - Eigenvalues and Eigenvectors - 7.6 Jordan Canonical Forms - Problems - Page 486: 4

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Since $A$ has eigenvalues $\lambda=2,2,2,2,2$, it will have seven Jordan canonical forms, such as: $$\begin{bmatrix} 2 & 0 & 0 & 0 & 0\\ 0 & 2 & 0 & 0 & 0\\ 0 & 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0\\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 2 & 1\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 1 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0\\ 0 & 0 & 0 & 2 & 1\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$ $$\begin{bmatrix} 2 & 1 & 0 & 0 & 0\\ 0 & 2 & 1 & 0 & 0 \\ 0 & 0 & 2 & 1 & 0\\ 0 & 0 & 0 & 2 & 0\\ 0 & 0 & 0 & 0 & 2 \end{bmatrix}$$