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

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 Herman Rubin Posts: 399 Registered: 2/4/10
Re: Tensor Definition
Posted: Jul 9, 2013 3:06 PM

On 2013-07-08, J.B. Wood <john.wood@nrl.navy.mil> wrote:
> 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"), 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 definition seems to exclude well-known dyadics (stress tensor,
> permeability tensor, etc) having 9-components that are constants (for
> the material involved.) That aside, I'm still having a problem grasping
> the foregoing definition. Thanks for your time and any comment. Sincerely,

That "definition" must have been written by a physicist. It is not
a definition of a tensor, but of a restricted type of tensor function,
with all coordinate spaces being of the same finite size.

A better definition of a tensor is an element of the function space
from a product of finite indices to a linear space, usually the
base field.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558