Description
Use Cauchy Schwartz inequality to prove the following inequalities. HInt: use the
default inner product in R
n
and R
m×n which are defined as < u, v >=
X
i
uivi
and < A, B > =
X
i
X
j
aijbij respectively.
1. Prove that X
i
|xi
| ≤ √
n
X
i
|xi
|
2
, for all x ∈ C
n
.
2. Prove thatX
i
X
j
|aij |
2
|bij|
|
3 ≤
X
i
X
j
|aij |
4
X
i
X
j
|bij |
6
, for all A, B ∈
C
m×n
.