# LINEAR ALGEBRA: Therom: If λ is an eigenvalue for At, then λ is an eigenvalue for A

May 29th, 2015
Studypool Tutor
Price: \$10 USD

Tutor description

We want to make a new matrix obtained by dividing each entry by the sum of all other entriws in the same column. Problem: What if page j doesn’t link to anything? Then you get a column of zeros

Word Count: 848
Showing Page: 1/6
Google's Page RankCumpute the probability that a "random surfer" will end up at a particular webpage.Ned to know the number of webpages - there are tracking sitessuppose there are 5 websites: 514Arrows represent page j (beginning) links to page i23Make a 5x5 matrixA=(Ai,j)5 I,j =1 where Ai,j 1 if page j links to page i0 otherwiseFor our example?0 0 0 0 1A = 1 0 1 0 00 1 0 0 01 0 1 0 01 0 0 0 0We want to make a new matrix obtained by dividing each entry by the sum of all other entriws in the same columnProblem: What if page j doesn't link to anything? Then you get a column of zerosSolution- change all entries in that colum to one to get a matrix A'0 0 0 1 1A' = 1 0 1 1 0Now divide the entries by column sums to get B0 1 0 1 01 0 1 1 01 0 0 1 0 0 0 0 1/5 1B = 1/3 0 1/2 1/5 0We assume that our "random sufer" has a certain tolerance for just 0 1 0 1/5 0clicking on links1/3 0 1/2 1/5 01/3 0 0 1/5 0Here, we assume it is .85 This means with probability .15 (15%) our random surfer gets bored and start at a new webpageReplace B with the matrix? C i,jEi,j = matrix with 1 in (i,j) position,zero in every other portionn = number of web pagesC = .85B + .03 =(.85/3) + .03=(.85/3) + (.09/3)=(.49/3)We get? .03 .03 .03 .2 .88.94/3 .03 .455 .2 .03C= .03 .88 .03 .2 .03.94/3 .03 .455 .2 .03.94/3 .03

## Review from student

Studypool Student
" Solid work, thanks. "

1822 tutors are online

### Other Documents

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors