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Topic: Tensor Definition
Replies: 16   Last Post: Jul 16, 2013 8:48 PM

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Shmuel (Seymour J.) Metz

Posts: 3,345
Registered: 12/4/04
Re: Tensor Definition
Posted: Jul 8, 2013 8:23 PM
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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 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.

>That definition seems to exclude well-known dyadics (stress tensor,
>permeability tensor, etc) having 9-components that are constants
>(for the material involved.)


Constant? Dont they vary, e.g., when there are compression waves?


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Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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