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Homework Help: Liouville Formula

  1. Nov 2, 2005 #1
    Would anyone be so kind as to offer a small hint for constructing a proof of:
    det(exp(A)) = exp(tr(A))
    where A is a square (diagonalizable) matrix and exp(A) = I + A + (1/2)A^2 + ...
     
  2. jcsd
  3. Nov 2, 2005 #2

    Galileo

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    As a first step, diagonalize A. That is, write it as A=CDC^(-1)
     
  4. Nov 2, 2005 #3
    Thank you

    Very nice. Of course (CDC^(-1))^n = CD^(n)C^(-1). The C and C^(-1) factor out and disappear then the rest just follows naturally. Thank you agin!:smile:
     
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