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Matrix is, roughly speaking,

a 2-dimensional rectangular array of numbers.

Then, I was wondering if there could exist a generalization of a matrix that consists of an n-dimensional higher-spacish rectangular array of numbers. For $d=3$, we can think of a cube $n\times n\times n$, whose every unit cube contains a number. Does linear algebra go as far as that? Or, will it stop at our 2-dimensional matrices? Why? Why not?

Ualibek Nurgulan
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    A matrix is more than a rectangular array: it also has addition and multiplication defined in particular circumstances. Addition is simple: pointwise addition if the two matrices are the same size and shape. Multiplication is rather more special, and you would need to define it in your new example – Henry Dec 12 '22 at 16:03
  • Yes, it is called a Tensor. Look it up. – user619894 Dec 12 '22 at 16:03

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