Euclidean vector spaces/Linear mapping/Norm/Obtained/Exercise

Let $V$ and $W$ denote Euclidean vector spaces, and let

$\phi :V⟶W$

be a linear mapping. Show that there exists a vector $v\in V$, $\Vert v\Vert =1$, such that

$\Vert \phi (v)\Vert =\Vert \phi \Vert$

holds.

Create a solution