/sci/ - Science & Math

>>11861358
IIRC it went something like this:
You have a ball flying in euclidean space. If you fix some coordinate system, you can give its velocity as a triple, that is, a vector in [math]\mathbb{R}^3[/math].
If you change your system of coordinates, by for example going [math](x, y, z) \rightarrow (y, x, z)[/math], then your speed vector's triple changes appropriately in the obvious way.
So essentially, you have a group [math]G[/math] acting by coordinate transformations, and it has a corresponding action (or, in physicist, a representation) on a vector space [math]V[/math] which gives the speed vector in new coordinates (and at the same point but in new coordinates).
A scalar, like temperature on the other hand, doesn't transform at all, it just assumes some value at a point.
IIRC a vector transforms like speed does.

I think that was it.