Consider a matrix-with-hole like below:
$$ \begin{bmatrix} None & x \\ y & 0 \end{bmatrix} $$
We can define two variants of means for the above object:
one is to calculate means by row first (None values do not count) then calculate the mean of means:
M1 = 1/2 * (x + 1/2 * (y + 0)) = x/2 + y/4
the other is to calculate means by columns first (None values do not count) then calculate the mean of mean:
M2 = 1/2 * (y + 1/2 * (x + 0)) = x/4 + y/2
If we generalize this kind of matrix-with-holes to an n-dim-tensor-with-holes, then there would be n! different orders of calculating the means.
My question is, is this kind of mathematical object well studied? Is there a name for these matrix/tensor with holes(missing elements)?
I explored https://en.wikipedia.org/wiki/List_of_matrices and it seems this kind of weird object is not qualified to be categorized as "matrix" and as a result it is really difficult to find the right keyword for it.
Thank you!