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Inverse of a fundamental matrix

  1. Dec 31, 2007 #1
    Hello, I have a little problem. I´ve calculated the fundamental matrix of a EDO system, such that:

    M(t) = P * exp( J*t)

    where J is a diagonal matrix:

    J = [-3 , 0 ; 0 , 1] and P = [1 , 1 ; 3 , -3]

    The problem arise when I try to find the inverse matrix of M. What I do is this

    As we know the inverse of a product is the product of the inverse, so firstly I find P[tex]^{-1}[/tex]. Then I look for the inverse of exp(J*t), that in this case is exp( -J*t). That´s all. Now, when I do the product of the two inverse matrix, the result is not the resul of the inverse of M. Can anyone tell me where ir my mistake?

    Thank you!
     
    Last edited: Dec 31, 2007
  2. jcsd
  3. Dec 31, 2007 #2
    The right formula is

    [tex]M=A\cdot B\Rightarrow M^{-1}=B^{-1}\cdot A^{-1}[/tex]

    Did you reverse the order of A, B?
     
  4. Dec 31, 2007 #3
    That was the problem :redface:. What a stupid mistake!!!

    Thank you very much!!
     
  5. Dec 31, 2007 #4
    I am glad that I helped! :smile:
     
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