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Is this correct about matrices

  • Thread starter Yegor
  • Start date
147
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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?
 

matt grime

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who says it is incorrect?
 

Hurkyl

Staff Emeritus
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[tex](BA)^{-1}=A^{-1}B^{-1}[/tex]
Yes, provided A and B are both invertible matrices...
 
147
1
[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]
 
147
1
Oh, yes. Now i see. Thank you very much, Hurky!
 

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