# Choice of vectors from basis in Gram-Schmidt process

Say I have a basis for $$\mathbb{c}^{2}$$ composed of the vectors $$(1,1), (4i,2i )$$ with complex inner product. When I construct my orthogonal basis using the Gram-Schmidt process how do I make a choice of which of these vectors are $$u_{1}$$ and $$u_{2}$$ because this will obviously have an impact when we carry out the inner product and swapping would give different answers.

• Why does getting different answers matter? – amd Jan 9 '19 at 20:01
• You pick whichever you think will make the calculations easier. There is no "correct" choice, because there is no "correct" or unique orthonormal basis. – Arturo Magidin Jan 9 '19 at 20:02
• The Gram-Schmidt process operates on an ordered basis, so whatever order your ordered basis is in. – user3482749 Jan 9 '19 at 20:06