# Are scalar/vector fields basically just “multi-valued” functions?

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 (x*y*2, x*y*2)


Is this basically it, or am I missing something?

• – Henricus V. Apr 7 '16 at 0:18
• Yes, that's correct. The notation merely stresses that the space may be high dimensional. – Oliver Apr 7 '16 at 0:18
• 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 7 '16 at 0:20
• 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 7 '16 at 8:40
• @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 7 '16 at 10:45