Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I'm stuck to prove Nilpotent Matrix

  1. Oct 17, 2006 #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. Oct 17, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Put it in jordan normal form and it all drops out. Alternatively just think about the characteristic poly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: I'm stuck to prove Nilpotent Matrix
  1. Nilpotent Matrix Proof (Replies: 8)

  2. Nilpotent Matrix Proof (Replies: 2)

Loading...