The Golden Ratio as the Dominant Eigenvalue of the Fibonacci Matrix — E8 Intelligence Research

{"FINDING:":[0],"The":[1,67,113,139],"golden":[2,115],"ratio":[3,88,116],"emerges":[4],"as":[5],"the":[6,10,118,133,155],"dominant":[7],"eigenvalue":[8,80],"of":[9,135,154],"Fibonacci":[11,24,71],"substitution":[12,68,140],"matrix,":[13],"linking":[14],"linear":[15],"algebra,":[16],"self-similarity,":[17],"and":[18,48],"quasicrystalline":[19],"inflation":[20],"symmetry.":[21],"|":[22,92],"MATH:":[23],"matrix":[25,69],"\\\\(":[26,39,49,60,75,81,89,98,103,108,122,136,143],"M":[27],"=":[28,41,43,51,53,62,100,105,110,124,126],"\\\\begin{pmatrix}1":[29],"&":[30,34],"1":[31,33],"\\\\\\\\":[32],"0\\\\end{pmatrix}":[35],"\\\\)":[36,47],"has":[37,78],"eigenvalues":[38,142],"\\\\lambda_1":[40],"\\\\varphi":[42,76,82,137],"\\\\frac{1+\\\\sqrt{5}}{2}":[44],"\\\\approx":[45,55],"1.618":[46],"\\\\lambda_2":[50],"-\\\\varphi^{-1}":[52],"\\\\frac{1-\\\\sqrt{5}}{2}":[54,125],"-0.618":[56,127],"\\\\).":[57,66,91,112,138],"Binet's":[58],"formula:":[59],"F_n":[61],"\\\\frac{\\\\varphi^n":[63],"-":[64],"(-\\\\varphi)^{-n}}{\\\\sqrt{5}}":[65],"for":[70],"tiling":[72],"(inflation":[73],"factor":[74],"\\\\))":[77],"Perron-Frobenius":[79],"\\\\),":[83,102,107,128],"with":[84],"eigenvector":[85],"components":[86],"in":[87],"1:\\\\varphi":[90],"CONNECTION:":[93],"Direct":[94],"geometric":[95],"harmony":[96],"—":[97],"\\\\varphi^{-1}":[99],"0.618":[101],"\\\\varphi^{-2}":[104],"0.382":[106],"\\\\varphi^2":[109],"2.618":[111],"twin":[114],"(from":[117],"\\"twin\\"":[119],"video)":[120],"is":[121,132],"\\\\psi":[123],"whose":[129],"absolute":[130],"value":[131],"reciprocal":[134],"matrix's":[141],"\\\\{\\\\varphi,":[144],"-\\\\varphi^":[145],"Author:":[146],"Andrew":[147],"Stewart":[148],"Caldin,":[149],"Independent":[150],"Researcher,":[151],"UK.":[152],"Part":[153],"E8":[156],"Intelligence":[157],"Research":[158],"series.":[159],"Platform:":[160],"e8intelligence.com":[161]}