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Math Help - Vectors notation

  1. #1
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    Vectors notation

    What do double bars around a vectors name indicate? For example they are used at the Triangle inequality page of wikipedia. I am struggling to understand a proof written elsewhere.
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    Quote Originally Posted by Stuck Man View Post
    What do double bars around a vectors name indicate? For example they are used at the Triangle inequality page of wikipedia. I am struggling to understand a proof written elsewhere.
    ||\bar{v}|| indicates the magnitude, or "norm" , of a vector ... i.e. its length.
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    Is it an alternative notation to single bars?
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    Quote Originally Posted by Stuck Man View Post
    Is it an alternative notation to single bars?
    actually, the single bar notation is the alternative.
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    I wonder why does the page I mentioned confuse things by using both notations in the same section?
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    Quote Originally Posted by Stuck Man View Post
    I wonder why does the page I mentioned confuse things by using both notations in the same section?
    If \alpha is a scalar and \vec{v} vector then <br />
\left\| {\alpha \vec{v}} \right\| = \left| \alpha  \right|\left\| \vec{v} \right\|
    Is that what you mean by using ‘both’ notations on the same page?
    If so those are not the same. One is the absolute value of a scalar(a number) the other is length of a vector.
    As was said, some authors use only the single bar for both concepts.
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    Also one possibility, which I doubt is the case, but is entirely possible, consider a vector of one dimension V = <-2> and the scalar -2, the following is true:
    ||V||=|-2|. This is so because ||V||=\sqrt{(-2)^2} = \sqrt{4} = 2 and |-2| = 2. So, in a strange abuse of notation, the absolute value of the componant of a one dimensional vector is equal to its magnitude. Now, I doubt that wikipedia would use such a rare case, and such an "abusive of notation" to denote this fact. I'm sure its highly more likely that its simply the alternative notation for the magnitude of a vector. But its interesting to see a relationship between the two notations based on the fact that:

    |a| = \sqrt{a^2}

    Thats my two cents, take it for what its worth.
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