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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You need to check three things. Which property are you struggling with ? The triangle inequality ?
Originally Posted by javax 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 I've done this on my blog (this is called the operator norm)--look here and here
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