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Homework Help: Linear Algebra Unique Factorization

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Assume that the matrix A is diagonalizable : A=PDP-1, where D is the diagonal matrix of eigenvalues. Show that this factorization is not always unique

    2. Relevant equations

    3. The attempt at a solution
    I have a couple of theories. The first being that since the matrix D can be reordered in any way as long as the eigenvalues are on the diagonal.
    The second is that A=P-1CP when C is the non diagonalized matrix.
  2. jcsd
  3. Jan 19, 2010 #2


    Staff: Mentor

    I like your first theory. The order of the eigenvalues on the main diagonal of D depends on the order of placement of eigenvectors in P.
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