Description
Instructions: Read textbook pages 37 to 38 and 43 to 45 before working on the
homework problems. Show all steps to get full credits.
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
.
