Do $\begin{bmatrix} 0&i&0\\0&0&1\\0&0&0 \end{bmatrix} $ and $\begin{bmatrix} 0&0&0\\-i&0&0\\0&1&0 \end{bmatrix} $ are similar.Is this True/false
Clearly both are nilpotent and one is conjucate transpose of other but how to know if they are similar.i'm stuck. Please help me
Hint: both matrices have the same characteristic polynomial $p(x)=x^3$, and for both that is also the minimal polynomial. What can you conclude about their Jordan canonical forms?