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Why are vectors written like this: ||w||

  1. Sep 25, 2010 #1

    Femme_physics

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    Is there a point to the double lines?
     
  2. jcsd
  3. Sep 25, 2010 #2

    Hurkyl

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    The symbol [itex]|| \cdot ||[/itex] (where the argument is placed where the dot is) is commonly used to represent the norm function on vectors.
     
  4. Sep 25, 2010 #3

    Femme_physics

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    There's no profound logic behind it then, right? Just the chosen symbol eh?
     
  5. Sep 25, 2010 #4
    It's often written with single lines: |w|. Single lines also denote the absolute value of a real number, and the absolute value (also called the norm, magnitude or modulus) of a complex number. Maybe the notation started life there and spread to vectors.
     
  6. Sep 25, 2010 #5

    D H

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    That symbol is used for absolute value and the determinant of a matrix. While it is sometimes used to denote a norm as well, but doing so is generally considered to be bad form.

    Back to the OP, then: [itex]||\text{whatever}||[/itex] just a symbol with a (somewhat) well-agreed upon meaning. The typical meaning is the Euclidean norm. There are however many ways (an infinite number of ways) to define the length of a vector. All are norms.
     
  7. Sep 25, 2010 #6

    HallsofIvy

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    First, vectors aren't written like that! The "magnitude" of a vector is written like that. And the symbol is intended to look like "absolute value" because the magnitude of a vector is similar to and is used like the absolute value of a number.
     
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