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I Finding the matrix inverse by diagonalisation

  1. Apr 25, 2016 #1
    How would you go about doing this, I see it so often quoted as a method, but no-where can I find an example

    This is what I was thinking

    D=P^(-1)AP

    Would it then follow that D^(-1)=P^(-1)A^(-1)P ?

    My reasoning being:

    DD^(-1)= P^(-1)APP^(-1)A^(-1)P
    identity matrix= P^(-1)AA^(-1)P=identity matrix

    and hence

    A^(-1)=PD^(-1)P^(-1)

    Just wondering if this is what they meant or if I've completely missed the point

    Manny thanks in advance :))
     
  2. jcsd
  3. Apr 25, 2016 #2

    blue_leaf77

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    Yes, because finding the inverse of a diagonal matrix with all-non-zero diagonal is very easy.
     
  4. Apr 25, 2016 #3
    Fab - thank you. I just wanted to check :)
     
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