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What is a vector valued in a function?

  1. Jan 2, 2014 #1
    What is a vector valued in a function? For example: ##f(\vec{r})##; or a vector valued in another vector, as: ##\vec{f}(\vec{r})##. What this means? How this kind of calculus is done?
  2. jcsd
  3. Jan 3, 2014 #2


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    The vector [itex] \vec{r} [/itex] is called a displacement vector.A vector from origin to some point.In such uses,they are interpreted as showing that point.So you should interpret it as a function which associates to point [itex] \vec{r} [/itex] a scalar [itex] f(\vec{r}) [/itex] or a vector [itex] \vec{f}(\vec{r}) [/itex].
  4. Jan 3, 2014 #3

    D H

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    A function is something that maps one space into another. If that other space is a vector space, the function is a "vector-valued function". For example, position as a function of time. The input to the function is time, a scalar. The output is a vector. Thus ##\vec x(t)## is a vector valued function. The input can also be a vector. For example, ##\vec F(\vec r) = -G m_1 m_2 \vec r/||\vec r||^3## also is a vector valued function. On the other hand, a function that maps from a vector space to a scalar space (e.g., potential energy as a function of position) is not a vector valued function.

    With partial derivatives.
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