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Linear Algebra Proof - Determinants and Traces

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove for an operator A that det(e^A) = e^(Tr(A))

    2. Relevant equations



    3. The attempt at a solution

    I have no idea how to start. Can someone give me a hint?

    In general the operator A represented by a square matrix, has a trace Tr(A) = Ʃ A (nn) where A (nn) is the nth row nth column. I don't know how to write the determinant in such a form that's understandable to myself and don't know how to compare them.
     
  2. jcsd
  3. Sep 16, 2012 #2
    How about A's Jordan form?
     
  4. Sep 16, 2012 #3
    I have absolutely no background in linear algebra except a very elementary class on matrix arithmetic/eigenvalue problems and this is part of our "review" for a quantum mechanics class! Very few of my classmates have seen this math before and can't answer, I'm desperate!

    Is this possible to solve this using very elementary steps? I've found an advanced proof that I have no idea how to understand. What is a Jordan form?
     
  5. Sep 16, 2012 #4
    The basic idea is that you consider A in the basis of its eigenvectors. Is that enough of a clue?
     
  6. Sep 16, 2012 #5
    Yes I figured it out. thank you greatly.
     
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