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.