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?

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