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In matrix theory(2-dimensional arrays), we can define addition, multiplication, rank and determinants etc.

I'm working on generalizing these properties to multidimensional arrays as many as possible. Are there any results in this direction? I'd really appreciate it if you could provide some references.

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    $\begingroup$ What you are looking for is en.wikipedia.org/wiki/Tensor. $\endgroup$
    – M.G.
    Commented Nov 26, 2020 at 11:23
  • $\begingroup$ It helps a lot, thank you! $\endgroup$
    – Richard
    Commented Nov 27, 2020 at 2:33

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Yes, many of them.

The keyword you should look for is tensors (note that it is used in a slightly different meaning in the physics literature, though).

I suggest to start from Kolda and Bader's 2009 SIREV review paper, for instance, or from Van Loan's lecture notes here.

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