Is it possible to transpose a (m,n) matrix in-place, giving that the matrix is represented as a single array of size m*n ?

The usual algorithm 

transpose(Matrix mat,int rows, int cols ){
    //construction step
    Matrix tmat;
    for(int i=0;i<rows;i++){
      for(int j=0;j<cols;j++){
       tmat[j][i] = mat[i][j];
      }
    }
 }

doesn't apply to a single array unless the matrix is a square matrix. If none, what is the minimum amount of additional memory needed??

EDIT: I have already tried all flavors of 

for(int i=0;i<n;++i) {
  for(int j=0;j<i;++j) {
     var swap = m[i][j];
     m[i][j] = m[j][i];
     m[j][i] = swap;
  }
}

And it is not correct. In this specific example, m doesnt even exist. In a single line matrix mat[i][j] = mat[i*m + j], where trans[j][i] = trans[i*n + j]

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