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 ?
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
I think that for a matrix is symmetric it must be square
answered 31 Mar '12, 11:22
My assumption for B matrix is
I think B is fairly trivial to answer given those, especially 1.
I'm less confident about my answers for A and C