Dimostrazione.
1.
$\frac{\mathbf{v}_{1}}{\vert\vert\mathbf{v}_{1}\vert\vert}= \cdots = \frac{\mathbf{v}_{t}}{\vert\vert\mathbf{v}_{t}\vert\vert}=1, \qquad$ e inoltre
$\frac{\mathbf{v}_{i}}{\vert\vert\mathbf{v}_{i}\vert\vert} \cdot \frac{\mathbf{v...
...}{\vert\vert\mathbf{v}_{i}\vert\vert\cdot \vert\vert\mathbf{v}_{j}\vert\vert}=0$.
2.
Sia $a_{1}\mathbf{v}_{1}+\cdots + a_{t}\mathbf{v}_{t}=0$, allora $\forall i=1,\ldots,t$:
$(a_{1}\mathbf{v}_{1}+\cdots + a_{t}\mathbf{v}_{t})\cdot \mathbf{v}_{i}=a_{1}\un...
...{v}_{i})+ \cdots+ a_{t}\underbrace{(\mathbf{v}_{t} \cdot \mathbf{v}_{i})}_{=0}=$
$=a_{i}(\mathbf{v}_{i} \cdot \mathbf{v}_{i})= a_{i}\underbrace{\vert\vert\mathbf{v}_{i}\vert\vert^{2}}_{>0}. \,$Quindi $a_{i}=0.$
c.v.d.