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Math Help - prove a linear transformation is invertible on R^n

  1. #1
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    co-norm of a linear transformation on R^n

    |\;| is a norm on \mathbb{R}^n.
    Define the co-norm of the linear transformation T : \mathbb{R}^n\rightarrow\mathbb{R}^n to be
    m(T)=inf\left \{ |T(x)| \;\;\;\; s.t.\;|x|=1 \right \}
    Prove that if T is invertible with inverse S then m(T)=\frac{1}{||S||}.

    (I think probably we need to do something with the norm, but I still can't get it... So thank you.)
    Last edited by ianchenmu; March 15th 2013 at 11:21 AM.
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  2. #2
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    Re: prove a linear transformation is invertible on R^n

    Hey ianchenmu.

    Is it possible to relate the norm to the determinant?
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