Let us look at examples for several values of n:

**n = 1: **Take **y** = (6).

Then ||**y**|| = 36^{1/2} = 6.

Thus, when n = 1, ||**y**|| is just the absolute value of the single coordinate of **y**.
**n = 2: **Take **y** = (3, 4).

Then ||**y**|| = (9 + 16)^{1/2} = 5,

which is the distance from the point (3, 4) to the origin in the plane.
**n = 4: **Take **y** = (3, 1, 2, 2).

Then ||**y**|| = (9 + 1 + 4 +4)^{1/2} = 18^{1/2},

which is the distance from the point (3, 1, 2, 2) to the origin in Euclidean 4-space.
Just close this window to return to the lecture.