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Math Help - Norms

  1. #1
    Member javax's Avatar
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    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
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  2. #2
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    Re: Norms

    You need to check three things. Which property are you struggling with ? The triangle inequality ?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Re: Norms

    Quote Originally Posted by javax View Post
    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
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