Tanu R.
Posts:
640
Registered:
12/13/04


Re: Tensor Definition
Posted:
Jul 8, 2013 2:02 PM


J.B. Wood wrote: > On 07/08/2013 11:03 AM, Sam Sung wrote: >> J.B. Wood write: >> >>> 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, >> >> You might read this: http://en.wikipedia.org/wiki/Tensor >> > Hello, and thanks for responding. I read the Wiki entry prior to my OP. > I don't see the correlation to the Webster definition.
I read this as an example for the use of tensors.
> Given the > usual 3D orthonormal coordinate systems commonly used in physics and > engineering (rectangular, cylindrical, spherical) I can view unit dyads > (having "two directions" just as easily as unit vectors having but one > direction (x, y, or z) and a dyadic having a total of 9 components vice > 3. Still, that dictionary definition confounds me. Sincerely,
Tensors are/canbe used by more than this kind of stuff; see (the first sentence of) http://www.wolframalpha.com/input/?i=tensor
Be sure to also know manifolds and dual objects, understand covectors, Grassmann products, vector fields and their covector fields, nforms, volume elements and their integrals, understand that there is math without reference to any coordinate system, remember that a tensor Q_a...c^f...h with p lower and q upper indices for any p,q >= 0 is a multilinear function (or mapping) of p vectors A,...,C and q covectors F,...,H where Q(A,...,C; F,...,H) = A^a...C^c Q_a...c^f...h F_f...H_h.

