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{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 57 "Computing the Perron Eige
nvector of a Non-negative Matrix" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(linalg):\nDigits:=3;\n
" }{TEXT -1 256 "For the following matrix M, which is a rearrangement \+
of M2, we compute the egenvector corresponding to the largest eigenval
ue.  We also do this for the transpose of M.   If M = (M_\{ij\}), thin
k of m_\{ij\} at the number of times football team i beat team  j.\n" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 408 "M2:= matrix([[0,4,5,2,4,
7],[6,0,4,1,7,6],[5,6.0,0,9,5,5],\n[8,9,1,0,7,8],[6,3,5,3,0,8],[3,4,5,
2,2,0]]):\nM2t :=transpose(M2):\nR:= matrix([[0,0,1,0,0,0],[0,1,0,0,0,
0],[1,0,0,0,0,0],\n[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]]):\nM:= t
ranspose(evalm(R&*M2&*R));\nMt :=transpose(M);\nX:=vector([1,1,1,1,1,1
]);\n#W2:=evalm(M2&*X): L2:=evalm(M2t&*X): S2:=evalm(W2 + L2):\nW:=eva
lm(M&*X);\nL:=evalm(Mt&*X);\nS:=evalm(W + L);" }}}}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 48 "Loop to compute MX and then normalize the output" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "MainEigenvect := proc(Q,n)\n
local i,k,X,Y,Z,sum;\nX:=vector([1,1,1,1,1,1]);\nY:=evalm(X/6);" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "for k from 1 to n\ndo\n  X:=evalm(
Q&*Y):\n  sum:=0;\n  for i from 1 to 6\n  do \n    sum := sum+X[i];\n \+
 od;\n  Y:=evalm(X/sum);\nod;\n#RETURN(sum, evalm(Y));\nRETURN(evalm(Y
));\nend;\n" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "Do the computati
on." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "MainEigenvect(M,4);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "MainEigenvect(M,10);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "MainEigenvect(Mt,10);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "MainEigenvect(Mt,20);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "0" 0 }
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