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i have question related to Gram–Schmidt process, in this process there is used such procedure $proj_u(v)=\frac{(v,u)\cdot u}{(u,u)}$ where $(v,u)$ is defined as inner product,so my my question is if $v=(1,2,3)$ and $u=(0,2,1)$ then does this projection equal to $ \frac{(1,2,3)\cdot(0,2,1)}{ ((0,2,1)\cdot(0,2,1))}\cdot u$? or if we continue this procedure,first multiplication gives us $1\cdot 0+2\cdot 2+3\cdot1=7$, second would be $0\cdot0+2\cdot2+1\cdot1=5$ so $\frac 75\cdot u$? or is there another step or other procedure for this calculation?please help me

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up vote 1 down vote accepted

If you're only trying to find $\operatorname{proj}_u(v)$ then that's accurate.

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