I am reading Gelfand's Lectures in Linear Algebra. I have some questions here:
I am trying to understand how to construct the given vectors with an example:
$$A=\left( \begin{array}{ccc} -1 & -18 & -7 \\ 1 & -13 & -4 \\ -1 & 25 & 8 \\ \end{array} \right)$$
This matrix has a single eigenvector $(-5, -3, 7)$ and three repeated eigenvalues $\lambda_1,\lambda_2,\lambda_3=-2$.
- Questions: We have $e_1=f_1=g_1=(-5, -3, 7)$, right? Do we have $e_2,f_2,g_2$? I think the answer is "no".
Now I am trying to use this information with the following section of the book:
- Question: It's not very clear to me what I should do here. How do I obtain this Jordan block? I think we need to do some change of basis, but it's not clear what change of basis is that.