.. (לתיקייה המכילה) | ||
In Q1a: | |
The definition of m choose n ,where n>m, is 0. Notice that where n is graten or equal to m, the bound, according to the above definition, is trivial. |
In Q4: What is the dual space of C (C^\perp)? | |
As been defined in the first tutorial, it is the space of all the vectors that the inner product with every vector in c is 0. | |
קישור: Link: Ссылка: وصلة: | http://webcourse.cs.technion.ac.il/236605/Winter2011-2012/ho/WCFiles/tut1_hebrew.pdf |
In Q2: I don't understand what is the n dimensional grid. | |
Think of it like an hint. You are allowed to give any other example for set with m lines with the required number of pyramids. |
In Q2: What are \Omega_n, O_n? | |
It's like the regular Omega and O where n consider to be a constant |
In Q2: Can I assume that s is integer? | |
Yes |
In Q2: what is [s]? | |
{1,...,s} |
I cannot solve Q4 and Q2a. | |
Make sure you have the latest version of the HW |
In Q2b. We need to show that we can assume that each line in L passes through |P|/2m points. | |
We count only for pyramids. I.e. show that we can assume that each line in L passes through |P|/2m points in P. |
In Q6: Can I assume the field is finite? | |
No |
In Q2a: what does it "a line with starting point a"? | |
a line through a point a (as defined in the question) |
In Q2c: I think there is a typo in the definition of the gradient. | |
Yes. It is the vector of all the derivative of g according to the variable x_1 to x_n (and of course, not just x_1 to x_1) |
In Q7: I think that in the definition in the first paragraph it is supposed to be | |
Yes |
In Q2b: what exactly is "the general claim"? | |
"This bound is tight", i.e. P = O(m^{n/(n-1)}) |
In Q2f: By inner product of g's gradient and v_i did you mean g's gradient, evaluated at a ? | |
Yes |
In Q2(d), you say the gradient of g is 0 iff g is 0. This should be iff g is constant, I think. | |
You are right. The general claim is indeed "the gradient of g is 0 iff g is constant". In this case g is a polynomial that vanishes on K. Only In this case you should show that "the gradient of g is 0 iff g is 0" |
In Q1a: what are they "linear polynomials"? | |
Linear functions |
In Q1: Do we have some assumptions on the field? | |
No. It can be any field. |
In Q4: what is an "inner product" over finite filed? | |
Indeed the definition of inner product is only regarding R or C. In our case <a,b> = sum a_i * b_i. Notice that it can be the case where <a,a> = 0 even when a is not 0, but it is still symmetric and bilinear. |
In Q7: Does A suppose to be the normalized adjacency matrix? | |
Yes. Every element in A is either 0 or 1/d. |
In Q7: What is the definition of the part of u that parallel to v? | |
(<u,v>/<v,v>)*v |
In general: We are not allowed to consult with each other, but what about the internet? | |
You can check websites like wikipedia for general information about algebra. Looking for the answers on the net is, of course, forbidden. |
In Q5: ("kidbag" question) is it indeed sufficient to prove just one direction as written in the question: ( E... <=\epsilon), | |
In order to show that the output bit is close to uniform the bound indeed need to be in absolute value. It doesn't really matter, since any reasonable way to prove the claim will also prove the bound for the absolute value. It is recommended that you verify that your proof indeed works for the more general case. |
In general: How to submit the file? | |
You can submit it as lyx, word or ,if you are insist, as latex file. If you submit it as lyx (recommended) , please submit a pdf file too. |
In Q7: I think that in the definition in the first paragraph it is supposed to be | |
Yes |