# Thread: prove a linear transformation is invertible on R^n

1. ## 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.)

2. ## Re: prove a linear transformation is invertible on R^n

Hey ianchenmu.

Is it possible to relate the norm to the determinant?