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Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead.

From Wikipedia: a scalar field associates a scalar value to every point in a space

So basically this is just a function that returns a single value then?

# a scalar field in one dimensional space
def scalar_field(x):
    return x * 2

a scalar field in two dimensional space


def scalar_field(x,y):
    return x * y * 2

From Wikipedia: a vector field associates a vector to every point in space

So basically this is just a function that returns multiple values then?

# a vector field in one dimensional space
def vector_field(x):
    return (x*2, x*2)

a vector field in two dimensional space


def vector_field(x,y):
    return (xy2, xy2)

Is this all there is to this concept, or am I overlooking something?

AlanSTACK
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  • See http://math.stackexchange.com/questions/1222768/why-are-vector-valued-functions-well-defined-when-multivalued-functions-arent – Henricus V. Apr 07 '16 at 00:18
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    Yes, that's correct. The notation merely stresses that the space may be high dimensional. – Oliver Apr 07 '16 at 00:18
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    It is good though to avoid the phrase "multivalued function" though, which is usually used to suggest that you don't know which of the values will be returned. – Oliver Apr 07 '16 at 00:20
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    Your third example does not constitute a vector field on ${\mathbb R}^1$ but the parametric representation of a curve in ${\mathbb R}^2$. – The vectors of a vector field have the "dimension" of the base space. – Christian Blatter Apr 07 '16 at 08:40
  • @ChristianBlatter could you follow up with your post? maybe a code example as well? as I have said I am new to mathematics and many of these more abstract terms confuse me greatly w/o examples – AlanSTACK Apr 07 '16 at 10:45

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