A fixed size raw array matrix that is a 2D raw array

// A fixed size raw array matrix (that is, a 2D raw array).
#include <iostream>
#include <iomanip>
using namespace std;

auto main() -> int
{
    int const   n_rows  = 3;
    int const   n_cols  = 7;
    int const   m[n_rows][n_cols] =             // A raw array matrix.
    {
        {  1,  2,  3,  4,  5,  6,  7 },
        {  8,  9, 10, 11, 12, 13, 14 },
        { 15, 16, 17, 18, 19, 20, 21 }
    };
    
    for( int y = 0; y < n_rows; ++y )
    {
        for( int x = 0; x < n_cols; ++x )
        {
            cout << setw( 4 ) << m[y][x];       // Note: do NOT use m[y,x]!
        }
        cout << '\n';
    }
}

   1   2   3   4   5   6   7
   8   9  10  11  12  13  14
  15  16  17  18  19  20  21

C++ doesn’t support special syntax for indexing a multi-dimensional array. Instead such an array is viewed as an array of arrays (possibly of arrays, and so on), and the ordinary single index notation [i\] is used for each level. In the example above m[y] refers to row y of m, where y is a zero-based index. Then this row can be indexed in turn, e.g. m[y], which refers to the xth item – or column – of row y.

I.e. the last index varies fastest, and in the declaration the range of this index, which here is the number of columns per row, is the last and “innermost” size specified.

Since C++ doesn’t provide built-in support for dynamic size arrays, other than dynamic allocation, a dynamic size matrix is often implemented as a class. Then the raw array matrix indexing notation m[y] has some cost, either by exposing the implementation (so that e.g. a view of a transposed matrix becomes practically impossible) or by adding some overhead and slight inconvenience when it’s done by returning a proxy object from operator[]. And so the indexing notation for such an abstraction can and will usually be different, both in look-and-feel and in the order of indices, e.g. m(x,y) or m.at(x,y) or m.item(x,y).