I know every complex matrix can be made into a triangular matrix and characterization of Nilpotent matrix. Is this a better characterization of Nilpotent matrices? I tried to show M is a Nilpotent matrix but failed. Need help. Any Hint will be very helpful. Thank you.
This has little to do with characterisations of nilpotent matrices. Note that each entry of $(M+tN)^n$ is a polynomial in $t$ of degree at most $n$. If this polynomial has $n+1$ distinct roots, then...