Suppose I have a matrix $M$. From that matrix, I create a matrix $N$ by only keeping some rows of $M$. The rows to keep are given in a vector or set called $r$. Then I do the same with columns in vector/set $c$ in order to obtain matrix $Q$.
In a notation similar to Matlab or Numpy, this is realized by slicing:
N = M[r, :] # keep only rows whose index is in r
Q = N[:, c] # keep only columns whose index is in c
How does the mathematical notation for such a construct look? I'm also happy with a solution that does the slicing in one step.
I would write $N =(M_{i j})_{\substack{i \in r\\ 1 \le j \le m}}$ and $Q=(M_{i j})_{\substack{1 \le i \le n\\ j \in c}}$.