Prove the following: is not sub-multiplicative. Hint: Let A be a matrix whose entries are all equal to 1.  In Lemma 7.1, we proved that 2 ∞  Prove that 1 2 Hint: Consider using the CauchySchwarz...

Prove the following:

is not sub-multiplicative. Hint: Let A be a matrix whose entries are all equal to 1.

 In Lemma 7.1, we proved that

<sub>2

∞</sub>
 Prove that

<sub>1

2</sub>
Hint: Consider using the CauchySchwarz inequality involving vectors
 and

^T

b. Find a vector for which the inequalities in (a) are an equality.