# HW - 6-2 Summary and what about if N landmarks == N positions ?

 0 1 Hi all, from all the post I have read I ended up with those conclusions. I hope there are fine or can be confirmed by the Udacity staff. 1) A (or C) matrix depends strictly on the path (or landmarsk) so I think it is possible to answer using the assumption made by Sebastian: 1.a) very long path with many landmarks 1.b) for the purpose of this exercise consider that a block diagonal matrix must contain at least 2x2 size blocks in the diagonal 1.c) sparse => the majority of values is 0 1.d) diagonal => only the element along the diagonal are non-zero 1.e) block diagonal => for some small K number, even the off-diagonal elements might not be 0, but K is independent of the path links (here seems block diagonal means k-diagonal, an estension of the tri-diagonal) 1.f) symmetrical => A.trasponse() = A 2) For B matrix, in order to answer correctly, should we consider the case in which the number of landmarks is the same as the number of positions X and for each position the robot can see only one landmark that cannot be seen by anyone else position ? In other words, L0 is seen by X0, L1 is seen by X1, L2 by X2 and so on ? Thank you. asked 31 Mar '12, 08:18 Pasquale 722●7●21●46 accept rate: 72%

 0 I have the same question in regard to B Matrix, can each landmark be seen at 1 or 2 positions or can they be seen at alot of positions? answered 31 Mar '12, 10:37 Lei Qian 11●1
 0 More questions: *Block diagonal include diagonal? if I mark true for diagonal in any submatrice I have to mark block diagonal again. I think that for a matrix is symmetric it must be square answered 31 Mar '12, 11:22 Antonio Mari... 60●7 If you take into acocunt the assumption made by Sebastian 1.b which says for the purpose of this exercise consider that a block diagonal matrix must contain at least 2x2 size blocks in the diagonal then diagonal matrix it is not block-diagonal matrix because it doesn't have any 2x2 sub-matrices. (31 Mar '12, 11:42) Pasquale Thank, you're right On the other hand, What do you think about the necessity of having a square matrix in order for it to be simetric? I remember this from the school, but I don´t know if Sebastian considered that B.trasponse() = B is equivalent to symetric. Thank in avance (31 Mar '12, 12:49) Antonio Mari... Pretty sure your definition of symmetric is correct and the right one to use. (31 Mar '12, 12:52) Michael F @amer I think you are right, it should be a square. When Sebastian talks about symmetrical matrix he refers to Omega and not to B matrix. If you compute the trasponse of any non squared matrix you get matrix_non_squared.transpose() != matrix_non_squared (31 Mar '12, 13:41) Pasquale
 0 My assumption for B matrix is N is not equal to M (i.e anything you conclude if N==M isn't going to be the general case) (From the video) From each pose x0, x1....xN you can see a max of 3 out of the M landmarks. M >> 3 I think B is fairly trivial to answer given those, especially 1. I'm less confident about my answers for A and C answered 31 Mar '12, 11:49 Michael F 6.6k●7●30●68 Actually I feel the opposite. I am more confident on A and C. About B, the robot can see max 3 landmarks but it can also sees just 1. Think about for each position X0 the robot sees just L0, in X1 it sees just L1, in the X2 it sees just L2. In addition, let's suppose we have the same number of position and landmarks (so N == M). How will be the matrix B in this case ? (31 Mar '12, 13:33) Pasquale
 0 Would only this definition apply for block-diagonal matrix? what if we have some 2x2 blocks in the matrix which would overlap with other 2x2 blocks, but still they are on the main diagonal . is it accounted or not.. ? answered 31 Mar '12, 13:05 bumblesa 843●4●14●18 I think that Sebastian means as block diagonal also the k-diagonal matrices, a generalization of let's say tri-diagonal. So you can have off-diagonal members and a matrix with 2x2 blocks that overlap eachother on the diagonal. (31 Mar '12, 20:47) Pasquale
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