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Kip Thorne and Roger Blandford have an excellent introduction to tensors in their lecture notes on the Applications of Classical Mechanics. See sections 1.3 an
by splat 13y ago
Kip Thorne and Roger Blandford have an excellent introduction to tensors in their lecture notes on the Applications of Classical Mechanics. See sections 1.3 and 1.5:
http://www.pma.caltech.edu/Courses/ph136/yr2012/1201.1.K.pdf http://www.pma.caltech.edu/Courses/ph136/yr2012/1201.1.K.pdf
They emphasize the geometrical viewpoint in which tensors are just linear functions which map vectors onto vectors via the dot product. (Or more generally a rank-n tensor is a linear function which maps a vector onto a rank n-1 tensor via the dot product.) Throughout the entire course they eschew coordinate systems as much as possible since that tends to obscure the underlying math and physics.
- tedsanders 13y agoI found their introduction to tensors to be the most helpful I had ever read. Realizing that tensors are (or can be considered) functions that map vectors onto vectors was a big conceptual shift for me.
- Patient0 13y agoYes this paper is excellent. Far more comprehensible (to me) than the link at the top of this discussion. I guess it all depends on what you are already familiar with. I was familiar with vectors and functions of vectors, and the concept of a linear function. Therefore, "A rank-n tensor T is, by definition, a real-valued, linear function of n vectors." is a much better starting point for me.