From: John Phillips (phillips_at_[hidden])
Date: 2006-06-12 17:29:49
Andy Little wrote:
> AFAIK a vector classically represents a magnitude and direction without more
> information though, so the vector would be a position vector
Yes, anything that is a representation of a magnitude and a direction
is, in the math and physics senses of the word, a vector. Then there are
different representations of that vector, and that is where it is
possible for mixed units to appear.
In general, the only representation that has no concerns about mixed
units is cartesian coordinates in a space where the sense of scale in
all directions has the same units. The x, y and z positions in cartesian
3 space is an example. However, that same vector is represented by a
magnitude and 2 direction angles in spherical 3 space, and there is no a
priori reason to prefer one representation to another. The choice of
representation is always current application dependent.
Thus, for some not explicitly defined potential vector library it is
possible to have mixed units in even the simplest of applications.
There are also spaces where the units (or more accurately, the
dimensions) are not the same in all directions, so any vectors in those
spaces will have mixed units in any coordinate system. A commonly used
one is called "phase space" and it includes the position and momentum
variables for a system all in the same space. Thinking of them together
turns out to be quite important in some applications, so the example can
be quite meaningful for some people.
> Andy Little
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