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Math Help - Subordinate matrix norm properties proof

  1. #1
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    Subordinate matrix norm properties proof

    I have to show that the subordinate matrix norm is indeed a norm so I have to show that it satisfies the 3 properties.

    I've shown how it satisfies 2 of these properties but I'm stuck with this property:
    ||A|| > 0 unless A is the zero matrix.

    How do I show that this is true?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Subordinate matrix norm properties proof

    Quote Originally Posted by CourtneyMoon View Post
    ||A|| > 0 unless A is the zero matrix. How do I show that this is true?
    Hint If A=(a_{ij})\neq 0 there exists a_{kl}\neq 0 , so Ae_l\neq 0 where e_l is the l-th vector of the canonical basis.
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