
Re: Tensor Definition
Posted:
Jul 8, 2013 8:23 PM


In <kredj6$tsp$1@ra.nrl.navy.mil>, on 07/08/2013 at 09:07 AM, "J.B. Wood" <john.wood@nrl.navy.mil> 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 MerriamWebster'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 4vectors, to say nothing of the manifolds that pop up in String Theory.
>That definition seems to exclude wellknown dyadics (stress tensor, >permeability tensor, etc) having 9components that are constants >(for the material involved.)
Constant? Dont they vary, e.g., when there are compression waves?
 Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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