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Eigenvalues and Eigenvectors uniquely define a matrix

  1. Jul 1, 2009 #1
    Do a set of Eigenvalues and Eigenvectors uniquely define a matrix since you can produce a matrix [tex]M[/tex] from a matrix of its eigenvectors as columns [tex]P[/tex] and a diagonal matrix of the eigenvalues [tex]E[/tex] through [tex] M=P E P^{\dagger}[/tex]?
  2. jcsd
  3. Jul 1, 2009 #2
    i'm pretty sure the answer is yes
  4. Jul 1, 2009 #3
    It is a bit more complicated. What you say is true if you can diagonalize the matrix. But take a matrix with complex eigenvalues and you are quickly missing eigenvectors. look up algebraic vs. geometric multiplicity of eigenvectors
  5. Jul 1, 2009 #4
    Try it with 2 x 2 matrix [0, 1; 0, 0]
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