In linear algebra, a nilpotent matrix is a square matrix N such that
for some positive integer . The smallest such is called the index of ,[1] sometimes the degree of .
More generally, a nilpotent transformation is a linear transformation of a vector space such that for some positive integer (and thus, for all ).[2][3][4] Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings.