Thread: Vector Norm and Matrix Norm

Let x be a m - vector, A be an m x n matrix, show that

(1) infinity norm x <= 2nd norm x <= square root (m) * infinity norm x

(2) [1/square root(n)] * infinity norm A <=2nd norm A
<=
square root (m) * infinity norm A

Hello,

Originally Posted by tinng

Let x be a m - vector, A be an m x n matrix, show that

(1) infinity norm x <= 2nd norm x <= square root (m) * infinity norm x
(2) [1/square root(n)] * infinity norm A <=2nd norm A
<=
square root (m) * infinity norm A

Get back to the definitions of the norms :






You'll have to use two inequalities :
- Triangle inequality :
- Cauchy-Schwarz inequality :