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Math Help - Proof

  1. #1
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    Proof

    Does anyone know how to start this proof?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dwsmith View Post
    Does anyone know how to start this proof?
    By verifying the axioms. It's not too hard. What have you tried?

    For those unwilling to open PDFs the problem is verify that \|(x_1,\cdots,x_n)\|=\sum_{j=1}^{n}|x_j| is a norm.
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  3. #3
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    Well I know since it is ||x||_{1} that it is absolute value of every term x_{1}+x_{2}+...+x_{n}
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dwsmith View Post
    Well I know since it is ||x||_{1} that it is absolute value of every term x_{1}+x_{2}+...+x_{n}
    How about trying something like \|\alpha(x_1,\cdots,x_n)\|=\|(\alpha x_1,\cdots,\alpha x_n)\|=\sum_{j=1}^{n} |\alpha x_j|=|\alpha|\sum_{j=1}^{n}|x_j|=|\alpha|\|(x_1,\c  dots,x_n)\|
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  5. #5
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    Why do I want to prove scalar multiplication? It says show the sum is a norm on real^n.
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dwsmith View Post
    Why do I want to prove scalar multiplication? It says show the sum is a norm on real^n.
    Isn't that one of the axioms of a norm though?
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  7. #7
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    Ok I see how it is supposed to be done now.

    I was viewing it as a proof not axioms.
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