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$|\;|$ 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.)

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.)

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