- #1

Yegor

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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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- Thread starter Yegor
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- #1

Yegor

- 147

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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?

- #2

matt grime

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who says it is incorrect?

- #3

Hurkyl

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[tex](BA)^{-1}=A^{-1}B^{-1}[/tex]

Yes, provided A and B are both invertible matrices...

- #4

Yegor

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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]

- #5

Yegor

- 147

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Oh, yes. Now i see. Thank you very much, Hurky!

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