When making a projection of vector b on a, you take
a*aT/(aT*a) * b, but when in Gram-Schmidt, you take aT*b/(aT*a) *a, which are not the same, or are they? if they are, why?

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if a is column vector and b row vector, why is a*aT*b equal to aT*b*a

**= a*b^Ta Eh, 10 days ago. I doubt you'll see this or need it anymore. The reason why this holds is because of the symmetric property of the inner product. Specifically, spaces where you can define an inner product allow you to generate an orthogonal basis, which is all you're really doing in the Gram-Schmidt process, which is why they are equivalent.**

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