I am trying to understand the classic 1998 PageRank paper (from the Google guys). I'm confused here:
"In matrix notation we have R' = c(AR' + E). Since ||R'||_1 = 1, we can rewrite this as R' = c(A + E x 1)R' where 1 is the vector consisting of all ones"
How did the paper go from "(AR' + E)" to "(A + E x 1)R'"? I don't understand.
R' is a vector of size n, A is an n x n matrix, and E is a vector of size n.
OK, my coworkers cracked this one.
||R'||_1 = 1 (that's a subscript) means that all the terms of R sum to one rather than the typical euclidean magnitude.
"E x 1" is basic multiplication rather than a cross product (hard to tell which they meant), so (E times 1) times R' = E. E is n x 1 vector and 1 is a 1 x n vector of ones.