# Subordinate matrix norm properties proof

• Dec 6th 2011, 04:36 PM
CourtneyMoon
Subordinate matrix norm properties proof
I have to show that the subordinate matrix norm is indeed a norm so I have to show that it satisfies the 3 properties.

I've shown how it satisfies 2 of these properties but I'm stuck with this property:
||A|| > 0 unless A is the zero matrix.

How do I show that this is true?
• Dec 6th 2011, 10:28 PM
FernandoRevilla
Re: Subordinate matrix norm properties proof
Quote:

Originally Posted by CourtneyMoon
||A|| > 0 unless A is the zero matrix. How do I show that this is true?

Hint If $A=(a_{ij})\neq 0$ there exists $a_{kl}\neq 0$ , so $Ae_l\neq 0$ where $e_l$ is the l-th vector of the canonical basis.