In <email@example.com>, on 07/08/2013 at 09:07 AM, "J.B. Wood" <firstname.lastname@example.org> 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?
Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to email@example.com