Reading `This Week's Finds', http://math.ucr.edu/home/baez/week247.html, I'm informed that one should avoid picking coordinate systems and I'm unsure why that is the case. Any help on the matter is appreciated.
Linear algebra is all about vector spaces and linear maps. One of the lessons that gets drummed into you when you study this subject is that it's good to avoid picking bases for your vector spaces until you need them. It's good to keep the freedom to do coordinate transformations... and not just keep it in reserve, but keep it manifest!
Is there a simple example of when a choice of coordinates makes a difference in a result? ---thereby giving reason to avoid basis.
As Hermann Weyl wrote, "The introduction of a coordinate system to geometry is an act of violence".
Some googling has informed me that this issue is part of the larger notion of categorical naturality...