I am studying Jordan normal form and still trying to piece it together. Got stuck on this question.
Given a matrix representation of $T: V \rightarrow V$ in basis $A = (v_1,..,v_n)$ by \begin{bmatrix} \lambda & 0 & 0 & \dots & 0 & 0 \\ 1 & \lambda & 0 & \dots & 0 & 0 \\ 0 & 1 & \lambda & \dots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \dots & \lambda & 0 \\ 0 & 0 & 0 & \dots & 1 & \lambda \end{bmatrix}
In which basis $B$ has $M_{B}(T)$ Jordan normal form?
$M_{A}(T)$ has ones below the diagonal instead, so I am guessing there's an easy way to figure $B$ out.