1. The problem statement, all variables and given/known data Given basis |x>,|y>,|z> such that <x|x> = 2,<y|y> = 2,<z|z> = 3,<x|y> = i, <x|z> = i, and <y|z> = 2. Build an orthonormal basis|x'>,|y'>,|z'>. Each of the new basis vectors should be expressed in terms of the old ones multiplied by coeﬃcients. 2. Relevant equations |x'> = |x>/(<x|x>).5 (normalizing the original x ket) |y'> = |y> - <x'|y> |x'> 3. The attempt at a solution So far I have worked through that |x'> = (1/2).5|x> Using this result I have moved through the calculation of |y'> and found it equals |y> - (i/2) |x'> I am now trying to normalize this expression, but I am not sure what my inner product on the denominator will look like for this normalization, but my best guess is <y| - (i/2)<x'|y> - (i/2)|x'> but that does not look legitimate to me, so I am stuck here. How do I take the inner product of a bra and and ket, both of which are sums of two kets/bras?