
Re: Tensor Definition
Posted:
Jul 9, 2013 3:06 PM


On 20130708, 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 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 definition seems to exclude wellknown dyadics (stress tensor, > permeability tensor, etc) having 9components 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)4946054 FAX: (765)4940558

