Question 1
What is the main purpose of the Gram–Schmidt process?
Question 2
If $u_1=v_1$, what is the Gram–Schmidt formula for $u_2$?
Question 3
If $u_1$ and $u_2$ are orthogonal, what is $\operatorname{proj}_{u_1}(u_2)$?
Question 4
After Gram-Schmidt produces an orthogonal set $u_1,\dots,u_n$, how do you make it orthonormal?
Question 5
What can happen if the input vectors to Gram-Schmidt are linearly dependent?
