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Homework Help: Is this correct about matrices

  1. Jul 12, 2005 #1
    I know that for matrices A, B and C is correct to write: (AB)C=A(BC)
    Also [tex](BA)^{-1}=A^{-1}B^{-1}[/tex]
    Why [tex] (A^{T}A)^{-1}A^{T}=A^{-1}(A^{T})^{-1}A^{T}=A^{-1}[/tex] is not correct?
     
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  3. Jul 12, 2005 #2

    matt grime

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    who says it is incorrect?
     
  4. Jul 12, 2005 #3

    Hurkyl

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    Yes, provided A and B are both invertible matrices...
     
  5. Jul 12, 2005 #4
    [tex] (A^{T}A)^{-1}A^{T}[/tex] such expression comes in chapter about least squares aproximation.
    e.g. if we have inconsistent linear system Ax=b, then [tex] x=(A^{T}A)^{-1}A^{T}b[/tex] is best approximation. It is not equal to [tex] x=A^{-1}b[/tex]
     
  6. Jul 12, 2005 #5
    Oh, yes. Now i see. Thank you very much, Hurky!
     
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