1. ## Norms

Hello. I need some help on proving this:

If is $||\cdot||$ a vector norm on $R^{n}$, then prove that:
$||A||= \max_{||x||=1}||Ax||$ is a matrix norm.

Thank you very much for your time

2. ## Re: Norms

You need to check three things. Which property are you struggling with ? The triangle inequality ?

3. ## Re: Norms

Originally Posted by javax
Hello. I need some help on proving this:

If is $||\cdot||$ a vector norm on $R^{n}$, then prove that:
$||A||= \max_{||x||=1}||Ax||$ is a matrix norm.

Thank you very much for your time
I've done this on my blog (this is called the operator norm)--look here and here