{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdeco mpG%)QRdecompG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%( augmentG%(backsubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)ch arpolyG%)choleskyG%$colG%'coldimG%)colspaceG%(colspanG%*companionG%'co ncatG%%condG%)copyintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delro wsG%$detG%%diagG%(divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenv ectorsG%+eigenvectsG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffg ausselimG%*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG %(geneqnsG%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG %+htransposeG%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG% 'ismithG%*issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG %*leastsqrsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%' mulrowG%)multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG %&pivotG%*potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG% 'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smith G%,stackmatrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG %*sylvesterG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG% (vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "H:=matrix(2,2,[[2,-1],[-1,2]]);#prob2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HGK%'matrixG6#7$7$\"\"#!\"\"7$F+F*Q(pprint06\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvalues(H);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvectors(H);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7 %\"\"\"F$<#K%'vectorG6#7$F$F$Q(pprint06\"7%\"\"$F$<#KF'6#7$!\"\"F$Q(pp rint1F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#prob 3" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "H:=matrix(3,3,[[5,-2,0],[-2, 3,-1],[0,-1,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HGK%'matrixG6 #7%7%\"\"&!\"#\"\"!7%F+\"\"$!\"\"7%F,F/\"\"\"Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "eomgs:=evalf(eigenvalues(H)); #tiny imaginary part is from the numerical solutions." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&eomgsG6%^$$\"+$ 3X**G'!\"*$!\"\"!#5^$$\"+vbudTF,$!+SSDg')!#>^$$\"+g.G%H#F)$\"+SSDg')F2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "omega3:=evalf(sqrt(Re( eomgs[1])));omega1:=evalf(sqrt(Re(eomgs[2])));omega2:=evalf(sqrt(Re(eo mgs[3])));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'omega3G$\"+#Hwz]#!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'omega1G$\"+$He![k!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'omega2G$\"+1#)o9:!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "evalf(eigenvectors(H)); #same deal with the imaginary part" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%7%^$$\"+$3X**G'!\"* $!\"\"!#5$\"\"\"\"\"!<#K%'vectorG6#7%F+^$$!+9as\\kF*$F-F-^$$\")DC>7!\" )$!+&3X**G'!#>Q(pprint06\"7%^$$\"+vbudTF*$!+SSDg')F=F+<#KF06#7%F+^$$\" +@F6#H#F'$\"+?q7IVF=^$$\"+8gLBRF'$\"+(GIS5$!#=Q(pprint1F?7%^$$\"+g.G%H #F'$\"+SSDg')F=F+<#KF06#7%F+^$$\"+>)fGN\"F'$!+?q7IVF=^$$!+b-EX5F'$!+Sl >x9FTQ(pprint2F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "a1:=vec tor([1., 2.292112721, 3.923336013]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#a1GK%'vectorG6#7%$\"\"\"\"\"!$\"+@F6#H#!\"*$\"+8gLBRF.Q(pprint06 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a3:=vector([1., -.644 9725414, .12192425]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a3GK%'vect orG6#7%$\"\"\"\"\"!$!+9as\\k!#5$\")DC>7!\")Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "a2:=vector([1., 1.352859819, -1.045 260255]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#a2GK%'vectorG6#7%$\"\" \"\"\"!$\"+>)fGN\"!\"*$!+b-EX5F.Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# 7Z%(animateG%*animate3dG%-animatecurveG%&arrowG%-changecoordsG%,comple xplotG%.complexplot3dG%*conformalG%,conformal3dG%,contourplotG%.contou rplot3dG%*coordplotG%,coordplot3dG%,densityplotG%(displayG%*fieldplotG %,fieldplot3dG%)gradplotG%+gradplot3dG%,graphplot3dG%-implicitplotG%/i mplicitplot3dG%(inequalG%,interactiveG%2interactiveparamsG%.intersectp lotG%-listcontplotG%/listcontplot3dG%0listdensityplotG%)listplotG%+lis tplot3dG%+loglogplotG%(logplotG%+matrixplotG%)multipleG%(odeplotG%'par etoG%,plotcompareG%*pointplotG%,pointplot3dG%*polarplotG%,polygonplotG %.polygonplot3dG%4polyhedra_supportedG%.polyhedraplotG%*rootlocusG%,se milogplotG%*setcolorsG%+setoptionsG%-setoptions3dG%+spacecurveG%1spars ematrixplotG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "pointplot([[0,0],[a1[1],1],[a1[2],2 ],[a1[3],3]],connect=true); 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