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In abstract linear algebra you learn that vectorspaces (and in particular I

want to only consider ordered 2-tuples) have no natural coordinate system,

but you can introduce coordinate systems and describe vectors relative to

other vectors.

However, in physics, they often make the (1, 0) and (0, 1) vectors [2-tuple

vector objects themselves, *not* coordinates] parallel to the page edges,

regardless of the coordinate system used.

My question is: Is this merely convention?

I mean, it seems arbitrary that (1, 0) and (0, 1) get to be made parallel to

the page edges, although it is intuitive. So is this just the standard

intuitive way of interpreting the linear vector space of 2-tuples?

To clarify with an example, consider the ramp problems in physics.

There are two bases, the ground basis where we know gravity and the ramp

basis, where one of the axes is coincident with the ramp slope, and the

other orthogonal with the ramp slope.

We want to change the gravity vector to be relative to the ramp basis. The

ground system, which gravity is initially relative to, is taken to be the

standard basis. Is this necessary or just done for convenience?

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# Bases and coord systems

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