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Linear algebra: Jordan normal forms

  1. May 6, 2010 #1
    Suppose the characteristic polynomial of a matrix A is [tex]\lambda[/tex]^3([tex]\lambda[/tex]-1)([tex]\lambda[/tex]-2). If the nullity of A is two, what are the possible Jordan normal forms of A up to conjugation?


    I think that an example of a matrix with such characteristic polynomial is:

    0 0 0 0 0
    0 0 0 0 0
    0 0 0 0 0
    0 0 0 1 0
    0 0 0 0 2

    But then isn't the nullity 1 in this case?

    Otherwise, the possibilities for the above matrix are:

    0 1 0 0 0
    0 0 0 0 0
    0 0 0 0 0
    0 0 0 1 0
    0 0 0 0 2

    0 1 0 0 0
    0 0 1 0 0
    0 0 0 0 0
    0 0 0 1 0
    0 0 0 0 2

    0 1 0 0 0
    0 0 1 0 0
    0 0 0 1 0
    0 0 0 1 0
    0 0 0 0 2

    Am I correct?
    What should I do about the nullity which is 2?
     
    Last edited: May 7, 2010
  2. jcsd
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