Nilpotent matrix 幂零矩阵
In linear algebra, a nilpotent matrix is a square matrix N such that
for some positive integer k. The smallest such k is sometimes called the degree or index of N.
More generally, a nilpotent transformation is a linear transformation L of a vector space such that L = 0 for some positive integer k (and thus, L = 0 for all j ≥ k). Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings.
![M^q = 0\,](/Images/godic/202501/29/3a564ef2de50e5cc617d634e2bcea1752745.png")
![L^q = 0](/Images/godic/202501/29/fbdc478683b6b3135611238b5cfc4b642745.png")
对于某个整数q。