Hello. I need some help on proving this:

If is $\displaystyle ||\cdot||$ a vector norm on $\displaystyle R^{n}$, then prove that:

$\displaystyle ||A||= \max_{||x||=1}||Ax||$ is a matrix norm.

Thank you very much for your time

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- Jun 18th 2011, 02:56 PMjavaxNorms
Hello. I need some help on proving this:

If is $\displaystyle ||\cdot||$ a vector norm on $\displaystyle R^{n}$, then prove that:

$\displaystyle ||A||= \max_{||x||=1}||Ax||$ is a matrix norm.

Thank you very much for your time - Jun 18th 2011, 03:05 PMbobakRe: Norms
You need to check three things. Which property are you struggling with ? The triangle inequality ?

- Jun 18th 2011, 03:07 PMDrexel28Re: Norms