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The name of a variable in the $\mathbb{R}$ is called scalar.

Multiple scalars form a vector: $\mathbb{R}^n$

Two or more vectors form together a matrix: $\mathbb{R}^{n \times m }$

But what is the name of the 3 dimensional array of elments? ($\mathbb{R}^{n \times m \times k }$)

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    $\begingroup$ It can be called a multidimensional array or in some cases a tensor of order 3. $\endgroup$ – mathreadler May 20 '16 at 17:01
  • $\begingroup$ Hypermatrix $\endgroup$ – user137731 May 20 '16 at 17:08
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They are called Tensors, and in your case can be thought of as matrices whose entries are themselves matrices. Any higher dimensions are also called tensors and are distinguished by their "order" (number of dimensions)

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