I don't think your answer was clear. Yes - vector or matrix is just a low order tensor, and yes - you can use tensor computation for anything. But tensor decomposition is a very special operation which turns vector spaces into linguistic structure.
My answer to Do you see any connection between tensor decomposition and deep neural networks like transformers? https://www.quora.com/Do-you-see-any-connection-between-tensor-decomposition-and-deep-neural-networks-like-transformers/answer/Anima-Anandkumar-1?share=b6df0adb …
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A caveat worth adding: terms like "array", "matrix", "mapping", et alibi are used inconsistently across disciplines. My math, physics, & comp-sci classes defined "vector" in 3 different ways. Today I just call everything a bucket o' bits, with usage defined only by the code. :-)
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