On Tue, Jun 20, 2006 at 12:23:37AM +0700, Oleg Abrosimov wrote:
Gerhard Wesp wrote:
On Mon, Jun 19, 2006 at 10:04:21AM +0200, Matthias Troyer wrote:
As a physicist I am completely baffled and confused. What do you mean by rank of a quantity? Do you mean the size of a vector/matrix? If
I understood Olegs post about rank such that it was something that would allow to distinguish energy from torque, e.g. Is there such a thing? Off the top of my head, I cannot think of a situation where you might want to add energy to torque, even if in the SI system they have the same dimension (Nm).
Same thing for angular velocity [rad/s] and frequency (1/s). You probably don't want to add both, even if in SI they're both in s^-1. Is this maybe a deficiency of SI? Would it make sense to add the unit "radians" that is used colloquially anyway, to the system?
You are almost right, but in the end you've chosen a wrong direction.
There is a very good article in wikipedia about tensors in which tensor rank is also described: http://en.wikipedia.org/wiki/Tensor
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This problem can not be solved only inside dimensional analysis. I hope that it is clear from this post. The solution is to take into account the rank of quantity (rank is 0 -> scalar; rank is 1 -> vector, ...)
Having rank also solves the following problem I was wondering about: how do you define vector scalar multiplication in a sufficiently restrictive way. Without a notion of rank, matrix * vector could be ambiguous with scalar * vector since (matrix * x, matrix * y, matrix * z) would be a valid vector<matrix<T> >. Geoffrey