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

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 Mike Trainor Posts: 28 Registered: 4/21/13
Re: Tensor Definition
Posted: Jul 12, 2013 8:25 PM

On Mon, 08 Jul 2013 20:23:37 -0400, Shmuel (Seymour J.) Metz
<spamtrap@library.lspace.org.invalid> wrote:

>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.

Long, long time before that (vapourware?) physcists became
very comforatable with Hilbert spaces.