0
$\begingroup$

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?

$\endgroup$
  • $\begingroup$ See math.stackexchange.com/questions/1222768/… $\endgroup$ – Henricus V. Apr 7 '16 at 0:18
  • 1
    $\begingroup$ Yes, that's correct. The notation merely stresses that the space may be high dimensional. $\endgroup$ – Oliver Apr 7 '16 at 0:18
  • 2
    $\begingroup$ 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. $\endgroup$ – Oliver Apr 7 '16 at 0:20
  • 1
    $\begingroup$ 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. $\endgroup$ – Christian Blatter Apr 7 '16 at 8:40
  • $\begingroup$ @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 $\endgroup$ – AlanSTACK Apr 7 '16 at 10:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.