I'm stuck to prove Nilpotent Matrix

  1. Hi all,
    If a square matrix A of dimension n*n is a nilpotent matrix,i.e, A^k=0 for k>=m iff A has eigenvalues 0 with multiplicity n and index m or less. I did prove by induction if A^k=0 then all the eigenvalues are zero. I'm lost when I want to prove the oppesite, i.e, if all eigenvalues are zero then A^k=0? Please help
  2. jcsd
  3. matt grime

    matt grime 9,395
    Science Advisor
    Homework Helper

    Put it in jordan normal form and it all drops out. Alternatively just think about the characteristic poly.
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