
#1
Jan2208, 05:58 PM

P: 290

This is a very basic question, but one I keep getting confused on nonetheless. Can someone explain to me the difference between a scalar function and a vector function? I've been told that the only difference is in the way the quantities are regarded (one as scalars, the other as elements of a vector space) but I'm still quite confused... the terms keep popping up in relativity and I'm not sure what distinction I'm supposed to be making.




#2
Jan2208, 06:41 PM

P: 365

A scalar is a function that it's value is independent from the change of coordinates, while a vector has compontents that do dependent from the coordinate system.




#3
Jan2308, 04:25 AM

P: 111

A scalar function maps something to a scalar; a vector function maps something to a vector. So, to distinguish the two you simply ask what does the function return, a scalar or a vector.
Example: Let x and y be vectors. An example of a vector function of x would be f(x) = 5x. (f(x) returns a vector.) An example of a scalar function of x would be g(x) = x dot y (the dot product of x and y), a scalar. 



#4
Jan2308, 10:05 AM

P: 290

scalar or vector?
The difference between a vector and a scalar is very obvious... but I have to admit, I thought it was peculiar that in my electromagnetism book, a great distinction is made between the use of a vector function for surface integrals versus a scalar function for volume integrals. I wondered what would require one to have an output in a vector space, the other to not... physically, if I'm calculating an electric field or something, why should the electric field be a vector field in one dimension and a scalar field in the other?
But I like the response about coordinate change. That does make a lot of sense. 



#5
Jan2408, 08:25 AM

P: 111





#6
Jan2408, 03:40 PM

P: 6




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