1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Liouville Formula
  1. Liouville's Theorem (Replies: 8)