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If square of N is zero?

  1. Jul 18, 2009 #1
    if square of N is zero???

    1. The problem statement, all variables and given/known data
    Let N be 2x2 matrix such that N2=0. How can we prove either N=0 or N is similar over C to [0 0; 1 0]

    2. Relevant equations

    Two matrix is to be similar if A=P-1BP for invertible transformation matrix P



    3. The attempt at a solution
    I tried to multiply N by itself but I got square of indices and some complex variables so I think that's not working.
     
    Last edited: Jul 19, 2009
  2. jcsd
  3. Jul 18, 2009 #2

    Office_Shredder

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    Re: if square of N is zero???

    Start by noting that if N2 = 0 then N is non-invertible. What else can you conclude?
     
  4. Jul 19, 2009 #3
    Re: if square of N is zero???

    use of det(N)=ad-bc works while finding eigenvalue, thanks.
     
  5. Jul 20, 2009 #4

    HallsofIvy

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    Re: if square of N is zero???

    N2= 0 means that N2v= 0= 0v for all v. 0 is a double eigenvalue. N2v= N(Nv)= 0.
    Either Nv= 0 or Nv is in the null space of N.
     
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