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Re: non-vectors



"RAUBER, JOEL" wrote:

I recall
sitting in on a differential geometry class where in one of the early
lectures the professor asked what a vector is and how we represent it in
physics. I basically mentioned magnitude and direction and representation
by an arrow. He was quite happy and launched into a discussion (details of
which I forget) on how glad he was, despite my being a physics student, that
I hadn't talked about defining it in terms of transformation properties.


Note that I was not asked to "define" a vector, nor
did I attempt to do so. I mentioned some examples, and
I mentioned the transformation properties because I
was answering a question about the transformation
properties.

If I were going to define a vector, I would say something
about a normed Euclidean space. The transformation
properties are not the axioms of the space, but are fairly
direct consequences of the axioms.