Belitskii's canonical forms of upper triangular nilpotent matrices under upper triangular similarity

All indecomposable canonical forms are determined for upper triangular nilpotent matrices of size less than or equal to 7 under upper triangular similarity via Belitskii's algorithm. Furthermore, we show that there exists an indecomposable canonical form of upper triangular nilpotent n×n matrix which admits at least [n2]−2 parameters for n≥8.