what is nilpotent matrix?
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In linear algebra, a nilpotent matrix is a square matrix N such that
{\displaystyle N^{k}=0\,} N^{k}=0\,
for some positive integer k. The smallest such k is sometimes called the index of N.
More generally, a nilpotent transformation is a linear transformation L of a vector space such that Lk = 0 for some positive integer k (and thus, Lj = 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.
{\displaystyle N^{k}=0\,} N^{k}=0\,
for some positive integer k. The smallest such k is sometimes called the index of N.
More generally, a nilpotent transformation is a linear transformation L of a vector space such that Lk = 0 for some positive integer k (and thus, Lj = 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.
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