Mathematical formulation for index of the smallest element in a matrix

Question

I have a matrix $X$ with elements $x_{i,j}$ and need to identify the indices $(i',j')$ of the smallest element of the matrix.

From a coding perspective, this is not hard (writing in python I used numpy.where). However, I do not know how to write in the paper the procedure down in a mathematically correct way.

For now, I simply wrote simply

$i',j' ~\text{ where }~ x_{i',j'} = \min\left( X \right)$

but this seems odd to me.

Can somebody tell me a better way to formulate this mathematically correct (and if possible short)?

Answer 1

$$(i',j')=\arg\min_{i,j} x_{i,j}$$

Answer 2

I think the best way to explain your code is to use English. Just say

$(i',j')$ is the index of the least entry in matrix $X$.

"Mathematically correct" does not require a formula. The words are fine.