Nilpotent matrix
Mathematical concept in algebra / From Wikipedia, the free encyclopedia
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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.