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Math Help - numerical analysis (norm)

  1. #1
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    tehran
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    numerical analysis (norm)

    prove that if |.| is a vector norm, and if we define |x|'=a .|x| (a is a positive constant), then |.|' is a norm.

    * numerical analysis
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  2. #2
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    Re: numerical analysis (norm)

    There are three properties needed to be checked to make |.|' a vector norm.

    (I) |cv|' = a|cv| = a(c|v|) = c(a|v|) = c|v|'.
    (II) |v + w|' = a|v + w| <= a(|v| + |w|) = a|v| + a|w| = |v|' + |w|'.
    (III) if |v|' = 0, then a|v| = 0,|v| = 0, and v = 0 [this last 0, the zero vector.]

    In each case, the norm properties of |.| have been used to show that |.|' satisfy them as well.

    Hope this helps.
    Last edited by RBowman; December 1st 2012 at 05:13 AM. Reason: Made reading easier
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  3. #3
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    Re: numerical analysis (norm)

    thanks : )
    yea it works.
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