I would like to understand more about the tensors product/tensors and apart from the definition, I think it would be useful to understand first historical use or motivation of a tensors. For example vector spaces as they are defined today came quite lately historically after realizing that there are many structures in the mathematics that share common properties. So one does not necessarily have to understand the definition fully before he gets grasp of vector spaces by understanding first historical examples, from times when people did not have the concept of a vector space at all.

So I was wondering if this is same for the tensor products, and if so, what were the initial tensor products that were used? In other words what preceded/lead to the definition of tensors?

I have checked questions here and they seem to boil down to first definition and then examples. Closest one I found is this What is the history of the term "tensor"?, but again the answers start with the definition and/or how to understand/interpret it, but they are not about what preceded the definition. I would really like to follow the historical path.

  • $\begingroup$ See Michael Crowe, A History of Vector Analysis : The Evolution of the Idea of a Vectorial System (1967), Ch.2 for Hamilton and see Hamilton, ON QUATERNIONS (1844-50) , page 13 for the "first appearance". $\endgroup$ – Mauro ALLEGRANZA Nov 26 '16 at 11:38
  • $\begingroup$ let me allocate two or three names or concepts to dig: Grassmann, determinant, quadratic forms, multilinear maps, vectorspaces, wedge or exterior product, exterior derivative, vectorbundles, tensorbundles, curvature, relativity,... $\endgroup$ – janmarqz Nov 26 '16 at 22:28
  • $\begingroup$ Nice, will check those resources, thank you guys. $\endgroup$ – Sil Nov 27 '16 at 16:47

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