20. PageRank: calculate the PageRank of a 6-page network based on the following eigenvalues and eigenvectors outputs of its transition matrix. For example, you answer should like this: 524 163. This means page #4 is ranked as #1, the most popular page, and page #5 is the least popular page. ## eigen() decomposition ## Svalues ## [1] 1.00000000+0i 0.57619235+0i -0.42500000+0i -0.42500000-0i ## [5] -0.34991524+0i -0.08461044+0i ## ## Svectors ## [,1] ## [1,] 0.1477266+0i 0.5275837+0i [,2] [,3] -4.387326e-16-0.000000e+00i 8.319669e-16+8.865582e-23i -8.189675e-16-9.074520e-23i ## [2,] 0.7220372+0i 0.3036276+0i ## [3,] 0.1151117+0i 0.3536714+0i ## [4,] 0.1036678+0i -0.5100565+0i ## [5,] 0.3779186+0i -0.2465028+0i ## [6,] 0.5385341+0i -0.4283234+0i ## [,4] -7.071068e-01+0.000000e+00i 7.071068e-01+0.000000e+00i 0.000000e+00-1.385437e-08i [,5] [.6] ## [1,]-4.387326e-16+0.000000e+00i 0.02248148+0i 0.859403314+0i ## [2,] 8.319669e-16-8.865582e-23i -0.10476977+0i -0.213621380+0i ## [3,] -8.189675e-16+9.074520e-23i 0.11814940+0i -0.365908958+0i ## [4]-7.071068e-01+0.000000e+00i -0.62357781+01 -0.286060300+0i ## [5,] 7.071068e-01-0.000000e+00i 0.74828318+0i -0.002046736+0i ## [6,] 0.000000e+00+1.385437e-08i -0.16056648+0i 0.008234060+0i