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Given an $8\times 8\times 8 \times 8$ tensor $T$, what is the best terse notation for referring to the $8\times 8$ matrix formed by $T(2,3,i,j)$ for all $-1 < i < 8$ and $-1 < j < 8$. For example:

$$ T(2,3),\ T(2,3,0-7,0-7),\ T(2,3,*, *) $$

Is there a standard notation?

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I would use just regular matrix notation:

$$M \in M_{8\times8} : M_{ij} = T(2,3,i,j)$$

Or if you want you can also say:

$$M= \{T(2,3,i,j)\}_{i,j \in \{1,...,8\}}$$

I think that these two are the easiest ways to define the matrix.

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  • $\begingroup$ Not $\{1,\dots,8\}$ but rather $\{0,\dots,7\}$. $\endgroup$ Commented Aug 5 at 15:32

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