Homework assignment

1.

Homework
Exercise 1:
For A M n , proof:
(a) ||| A2 ||| ||| A ||| 2 , ||| A p ||| ||| A ||| p , p 2,3,...
(b) if A2 A then ||| A ||| 1
||| I |||
(c) if A is invertible , then ||| A |||
||| A |||
(d ) ||| I ||| 1.
1

2.

Homework
Exercise 2. Proof n || || is a matrix norm, where n
is the size of the matrix.
Exercise 3. The spectral norm ||| · |||2
||| A ||| 2 max
: is an eigenvalue of
is deduced by the l2 norm.
A A