A = RandomReal[{0, 1}, {10, 10}];
MatrixForm[A]
j = 1;
v = A[[j]];
e = v/Norm[v];
MatrixForm[e]
For[j = 1, j <= 10, j++, v - Sum[(v.e)*e, {i, 1, j - 1}]/Norm[v - Sum[(v.e)*e, {i, 1, j - 1}]]; Print[e]]