Description
1. Write down the default inner product in C
3
and show that the induced norm
corresponding to this default inner product is actually the 2-norm. Let
u =
Ñ
1 + i
2i
3 + i
é
, v =
Ñ
1
3 − i
−i
é
,
find the norm of u and the distance between u, v under the default inner product in C
3
.
2. Find the 1−, 2−,∞− norm unit balls in R
2
and sketch them. Find all the
x ∈ R
2
that satisfies kxk1 = kxk2 = kxk∞ = 1.
