>>17 補足
良い機会なので、下記を補足します
下記が、分かり易い
https://kconrad.math.uconn.edu/blurbs/ Expository papers KEITH CONRAD
Linear/Multilinear algebra
(下記以外にTensor products II、Fields and Galois theoryでSeparable extensions and tensor products、Splitting fields and tensor products のpdfがあります)
https://kconrad.math.uconn.edu/blurbs/linmultialg/tensorprod.pdf TENSOR PRODUCTS I KEITH CONRAD
Ｐ2
Here is a brief history of tensors and tensor products.
Tensor comes from the Latin tendere, which means “to stretch.”
In 1822 Cauchy introduced the Cauchy stress tensor in continuum mechanics, and in 1861 Riemann created the Riemann curvature tensor in geometry, but they did not use those names.
In 1884, Gibbs [7, Chap. 3] introduced tensor products of vectors in R3 with the label “indeterminate product”*3 and applied it to study strain on a body.
He extended the indeterminate product to n dimensions in 1886 [8].
Voigt used tensors to describe stress and strain on crystals in 1898 [25], and the term tensor first appeared with its modern physical meaning there.*4
In geometry Ricci used tensors in the late 1800s and his 1901 paper [22] with Levi-Civita (in English in [15]) was crucial in Einstein’s work on general relativity.
Wide use of the term “tensor” in physics and math is due to Einstein; Ricci and Levi-Civita called tensors by the bland name “systems”.
The notation ⊗ is due to Murray and von Neumann in 1936 [17, Chap. II] for tensor products (they wrote “direct products”) of Hilbert spaces.*5
The tensor product of abelian groups A and B, with that name but written as A◦B instead of A⊗Z B, is due to Whitney [27] in 1938. Tensor products of modules over a commutative ring are due to Bourbaki [2] in 1948.
脚注
*3 Gibbs chose that label since this product was, in his words, “the most general form of product of two vectors,” as it is subject to no laws except bilinearity, which must be satisfied by any operation deserving to be called a product. In 1844, Grassmann created a special tensor called an “open product” [20, Chap. 3].
*4 Writing i, j, and k for the standard basis of R3, Gibbs called a sum ai⊗i+bj⊗j+ck⊗k with positive a, b, and c a right tensor [7, p. 57], but I don’t know if this had an influence on Voigt’s terminology.
*5 I thank Jim Casey for bringing [17] to my attention.
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