# Norms

• June 18th 2011, 02:56 PM
javax
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
• June 18th 2011, 03:05 PM
bobak
Re: Norms
You need to check three things. Which property are you struggling with ? The triangle inequality ?
• June 18th 2011, 03:07 PM
Drexel28
Re: Norms
Quote:

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