How to Express Stacking Process of Vectors Mathematically

Question

I have this multi-dimensional matrix (5 * 5):

X= [ [ 1,1,1,1,1] , [2,2,2,2,2] , [3,3,3,3,3], [4,4,4,4,4] , [5,5,5,5,5]] 

I want to extract certain rows and columns like the following:

row at index 0 : [1,1,1,1,1]
row at index 3: [4,4,4,4,4] 
column at index 1: [ 1,2,3,4,5] (after transposing it to be a row vector)

Then , stacking them upon each other to form the following matrix (3*5):

Y = [ [1,1,1,1,1] , [4,4,4,4,4] , [1,2,3,4,5] ]

The question: how to express this stacking process mathematically (given: X is a square matrix, and the index of selected rows and columns should be arbitrary for generalization purpose)!

Answer 1

Suppose $M$ is the matrix.
Let $M_{(i)}$ denote the $i$th-index column of $M$, and $M^{(j)}$ denote the $j$th-index row of $M$.

Let $M_{(i)}^{{}^{\Large T}}$ denote the the transpose of $M_{(i)}$.

Then, $N$, the last matrix in your question can be written as: $$N = \begin{bmatrix} M^{(0)} \\ M^{(3)} \\ M_{(1)}^{{}^{\Large T}} \end{bmatrix}$$