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Matrix simplification

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Simplify

    A = HG(FHG)[tex]^{-1}[/tex]FG

    2. Relevant equations

    None

    3. The attempt at a solution

    Well (FHG)^-1 is really just F^-1 H^-1 G^-1
    Therefore A = HGG[tex]^{-1}[/tex]H[tex]^{-1}[/tex]F[tex]^{-1}[/tex]FG
    GG^-1 = I
    FF-1 = I

    Therefore A = HIH[tex]^{-1}[/tex](IG)

    The book now simplifies to HH[tex]^{-1}[/tex]G

    I understand all the steps and the ending step, but I don't get how they got rid of the two I's

    I X I = I (Identity Matrix), so where did it disappear to?

    The final answer is: A = G

    Thanks
     
  2. jcsd
  3. Oct 25, 2007 #2
    Urgh, silly me, solved.

    Identity matrix multiplied by another matrix just returns that matrix I forgot.

    Silly problem. Sorry.
     
  4. Oct 25, 2007 #3
    Not really. (FHG)^-1 = (G^-1)*(H^-1)*(F^-1).
     
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