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Homework Help: A question in finding a invert of a certain operator

  1. Mar 8, 2008 #1
  2. jcsd
  3. Mar 8, 2008 #2

    HallsofIvy

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    You are given that A2- A+ I= 0. Just basic algebra tells you that is the same as I= A- A2= A(I- A). Now, stop worrying about formulas, etc. and think about what A-1 means.
     
  4. Mar 8, 2008 #3
    it means that if we take the image of a certain basis
    and put it into the A^-1 we get the original basis

    how its gonna help me??

    thought of certain solution of making some basic multiplication
    operations

    i got the resolt

    A^-1=I-A
    is it ok??
     
    Last edited: Mar 8, 2008
  5. Mar 8, 2008 #4

    HallsofIvy

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    ?? No, A-1 doesn't mean anything like that: it means the linear operation that "undoes" A. A-1Ax= x and AA-1x= x.

    My point was that A(I- A)= I shows that I -A does exactly what we want of the inverse: AA-1= I. Since A(I-A)= I, (and inverses are unique), A-1= I- A.
     
  6. Mar 8, 2008 #5
    so what is the answer??
    what is the value of A^-1
     
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