# Do we consider a point in a coordinate system to be a scalar?

• I
Gold Member
Knowing that a scalar quantity doesn't change under rotation of a coordinate system. Do we consider a point in a Cartesian coordinate system (i.e. A (4,5)) a scalar quantity? If yes, why do the components of point A change under rotation of the coordinate system?
According to my understanding, the point A (4,5) is not considered scalar. Am I right?

fresh_42
Mentor
2021 Award
Knowing that a scalar quantity doesn't change under rotation of a coordinate system. Do we consider a point in a Cartesian coordinate system (i.e. A (4,5)) a scalar quantity? If yes, why do the components of point A change under rotation of the coordinate system?
According to my understanding, the point A (4,5) is not considered scalar. Am I right?

A point is a certain location, here at the coordinates (4,5). We need them to specify it, i.e. to assure that we are talking about the same location. We do this in vector form, that is by its distance and direction from another location which we earlier agreed upon calling the origin. So the description is by a vector, the location itself is not.

As a location, it is neither a vector nor a scalar. A scalar would be a single valued valuation, a number. In case every point has such a valuation, e.g. the temperature, this valuation would be the scalar and the set of all pairs (point , temperature) would be a scalar field. You see, that the point itself isn't called a scalar.

So scalars, vectors, matrices, tensors are what happens at a certain location, they can be evaluated at this location or they are simply attached to this location. Their nature, however, is different from the nature of the point, the location. That's more or less the physical point of view. Mathematically a point is just a zero-dimensional object that has nothing to do with scalars or vectors. It's not even located anywhere as long as we do not make assumption on how to describe it.

jedishrfu
Mentor
A scalar quantity is a value associated with a point. As an example, on a weather map the temperatures of various places would be scalars.

temp=T(latitude,longitude)

More on scalars:

https://hepweb.ucsd.edu/ph110b/110b_notes/node2.html