8阶上三角幂零矩阵在上三角变换下的Belitskii标准形

Belitskii’s canonical forms of upper triangular nilpotent matrices of order8 under upper triangular similarity

通过对算法进行计算机编程,计算8阶上三角幂零矩阵在可逆上三角矩阵变换下的所有402个不可分解标准形,其中333个标准形不含参数,有65个标准形仅含1个参数,有4个标准形含2个参数.

Based on the Python procedure of Belitskii algorithm,all the indeconposable Belitskii's canonical forms of upper triangular nilpotent matrices of order 8 under upper triangular similarity were calculated.It is shown that there are 402 indecomposable Belitskii's canonical forms,where there are 333 non-parameterized indecomposable Belitskii's canonical forms,65 one-parameterized ones and 4 two-parameterized ones.