>In <firstname.lastname@example.org>, on 07/08/2013 > at 09:07 AM, "J.B. Wood" <email@example.com> said: > >>Hello, all. Just when I think I've got a good handle on tensors >>(after painstakingly reading and working problems in Louis Brand's >>"Vector and Tensor Analysis"), > >As I recall, that book was written back when it was common to describe >tensors in terms of the way that their components changed under a >coördinate transformation. The modern view is more abstract and, IMHO, >easier to understand. > >>I come across the following in Merriam-Webster's >>Collegiate Dictionary: >>"A generalized vector with more than three components each of which >>is a function of an arbitrary point in space of an appropriate >>number of dimensions" > >That sounds positively 19th Century; I certainly don't know of any >mathematician who would assume that a vector is 3 dimensional, and >physicists routinely deal with 4-vectors, to say nothing of the >manifolds that pop up in String Theory.
Long, long time before that (vapourware?) physcists became very comforatable with Hilbert spaces.