This exercise shows that the formulas derived in Example 3 of Section 3.6.2 apply to any vector norm. Assume D is a diagonal  ×  matrix, with diagonal entries d 1 , d 2 , ··· , d n . (a) Show that ||...

This exercise shows that the formulas derived in Example 3 of Section 3.6.2 apply to any vector norm. Assume
D
is a diagonal
 ×
 matrix, with diagonal entries
d
₁,
d
₂, ··· ,
d_n
.

(a) Show that ||A||
_∞

= max{ |d
₁|, |d
₂|, ··· , |d_n
| }.

(b) Assuming the
d_i
’s are not zero, show that

(c) Show that

Example 3

Suppose
A
is a diagonal matrix 3 × 3, which means it can be written as