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The word tensor has become more ambiguous during the time. Before 1900, the use of the word tensor was consistent with its etymology, because it was used only
by adrian_b 3y ago
The word tensor has become more ambiguous during the time.
Before 1900, the use of the word tensor was consistent with its etymology, because it was used only for symmetric matrices, which correspond to affine transformations that stretch or compress a body in certain directions.
The square matrix that corresponds to a general affine transformation can be decomposed into the product of a tensor (a symmetric matrix which stretches) and a versor (a rotation matrix, which is antisymmetric and which rotates).
When Ricci-Curbastro and Levi-Civitta have published the first theory of what now are called tensors, they did not define any new word for the concept of a multidimensional array with certain rules of transformation when the coordinate system is changed, which is now called tensor.
When Einstein has published the Theory of General Relativity during WWI in which he used what is now called tensor theory, for an unknown reason and without any explanation for this choice he has begun to use the word "tensor" with the current meaning, in contrast with all previous physics publications.
Because Einstein has become extremely popular immediately after WWI, his usage of the word "tensor" has spread everywhere, including in mathematics (and including in the American translations of the works of Ricci and Levi-Civita, where the word tensor has been introduced everywhere, despite the fact that it did not exist in the original).
Nevertheless, for many years the word "tensor" could not be used for arbitrary multi-dimensional arrays, but only for those which observe the tensor transformation rules with respect to coordinate changes.
The use of the word "tensor" as a synonym for the word "array", like in ML/AI, is a recent phenomenon.
Previously, e.g. in all early computer literature, the word "array" (or "table" in COBOL literature) was used to cover all cases, from scalars, vectors and matrices to arrays with an arbitrary number of dimensions, so no new words are necessary.