Properties of Norm

Theorem

Let

• $\mathbf{v}$ vector in $R^n$
• $k$ any scalar

Then

• $||\mathbf{v}||\ge 0$
• $||\mathbf{v}||=0⟺\mathbf{v}=0$
• $||k\mathbf{v}||=|k|||\mathbf{v}||$