Example:

Consider the vector-difference example shown in Fig.5.7. The norm of the difference vector $w=x-y$ is

$$\Vert w\Vert \isdef \Vert x-y\Vert \isdef \Vert(2, 3) - (4, 1)\Vert = \Vert(-2, 2)\Vert = \sqrt{(-2)^2 + (2)^2} = 2\sqrt{2}.$$

Figure 5.7: Length of a difference vector.