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Question 1 - guidance
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We reccomend using the book by Dahlqvist & Bjork for answering this question. |
Question 2 seif dalet - clarification
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t0 is a parameter just like the rest. You should show that for every alpha and beta, there exists A and t0, that make the two expressions equal. After that you are asked if the second expression can be approximated, AS IT IS, using the algorithms taught in class (just like sections aleph and bet) |
Question 4
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Orthogonal vectors (with respect to the standard inner product) means that the cosine of the angle between the vectors is 90 degrees. That means: <u,v> = |u|*|v|*cos(alpha) - where alpha is the angle between u and v and the absolute value is the Euclidean length of them (also that is their l2 norm). Therefore, you should measure if Gram-Schmidt succeeded by calculating cos(alpha), or by calculating the inner product between the vectors AFTER NORMALIZING them. Then you should explain what happened. Note that if the vectors u,v are OF LENGTH 1 and <u,v> is of machine precision order, then u and v are considered orthogonal. |