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Math Help - How to understand the two vertical lines ||

  1. #1
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    How to understand the two vertical lines ||

    Hello I read the following equation
    Imageshack - log.gif
    but I do not understand what the
    || (what ever is inside) ||2 (with the 2 as a small number -- called index?)


    could you please help me understand what this is about?

    I would like to thank you in advance for your help
    Best Regards
    Alex
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  2. #2
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    That would be the 'length'
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  3. #3
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    || \mathbf{a} || is a notation that represents the "length" of a vector \mathbf{a}. In your expression, \mathbf{x} - \mathbf{x}_r is the vector whose length is being calculated.

    Since "length" can be defined in a number of ways, the subscript 2 indicates that the length is calculated using the Euclidean norm. So, ||\mathbf{x} - \mathbf{x}_r||_2 means that you should find the length of the vector \mathbf{x} - \mathbf{x}_r as defined by the Euclidean norm.

    The Euclidean norm is the most intuitive definition of length. For example, if you have a vector (4,-3), its Euclidean length would be 5. You can conceptualize this as the distance between the point (4,-3) and the origin.
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  4. #4
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    Quote Originally Posted by drumist View Post
    || \mathbf{a} || is a notation that represents the "length" of a vector \mathbf{a}. In your expression, \mathbf{x} - \mathbf{x}_r is the vector whose length is being calculated.

    Since "length" can be defined in a number of ways, the subscript 2 indicates that the length is calculated using the Euclidean norm. So, ||\mathbf{x} - \mathbf{x}_r||_2 means that you should find the length of the vector \mathbf{x} - \mathbf{x}_r as defined by the Euclidean norm.

    The Euclidean norm is the most intuitive definition of length. For example, if you have a vector (4,-3), its Euclidean length would be 5. You can conceptualize this as the distance between the point (4,-3) and the origin.
    I would like to thank you for your helpful post
    So it is enough to say that it refers to the Euclidean distance. I am still wondering why some texts wants to make life that hard when there are always simple ways to express things.
    Best Regards
    Alex
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  5. #5
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    What is so "hard" about that notation?

    What level text was this? There is usually a list of symbols, either in the very front or very back of the text book for an introductory text. In a more advanced text, of course, you would be expected to already know standard notation.
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