{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRde compG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG% (backsubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%) choleskyG%$colG%'coldimG%)colspaceG%(colspanG%*companionG%'concatG%%co ndG%)copyintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(delrowsG%$detG %%diagG%(divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eigenvectorsG%+ eigenvectsG%,entermatrixG%&equalG%,exponentialG%'extendG%,ffgausselimG %*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqns G%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htransp oseG%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG% *issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacianG%*leastsq rsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%) multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG% *potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG% )rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smithG%,stackm atrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swaprowG%*sylvest erG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotentG%(vectdimG %'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "A1 :=matrix([[omega1^2+omega2^2,-omega2^2],\n[-omega2^2,omega1^2+omega2^2 ]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G-%'matrixG6#7$7$,&*$)%'o mega1G\"\"#\"\"\"F/*$)%'omega2GF.F/F/,$F0!\"\"7$F3F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvals(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)%'omega1G\"\"#\"\"\",&F#F'*&F&F')%'omega2GF&F'F'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvects(A1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7%*$)%'omega1G\"\"#\"\"\"F(<#-%'vectorG6#7$F (F(7%,&F$F(*&F'F()%'omega2GF'F(F(F(<#-F+6#7$!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "A2:=matrix([[2*omega0^2,-omega0^2,0],[-om ega0^2,2*omega0^2,-omega0^2],\n[0,-omega0^2,2*omega0^2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G-%'matrixG6#7%7%,$*&\"\"#\"\"\")%'omeg a0GF,F-F-,$*$F.F-!\"\"\"\"!7%F0F*F07%F3F0F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvects(A2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 %7%,$*&\"\"#\"\"\")%'omega0GF&F'F'F'<#-%'vectorG6#7%!\"\"\"\"!F'7%*&,& F&F'*$F&#F'F&F'F'F(F'F'<#-F,6#7%F'*&,&F2F/*&F&F'F(F'F'F'F)!\"#F'7%*&,& F&F'F4F/F'F(F'F'<#-F,6#7%F'*&,&F?F/*&F&F'F(F'F'F'F)F=F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A3:=matrix([[2,-1,0],[-1,2,-1],[0,- 1,2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A3G-%'matrixG6#7%7%\"\"# !\"\"\"\"!7%F+F*F+7%F,F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvects(A3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7%\"\"#\"\"\"<# -%'vectorG6#7%!\"\"\"\"!F%7%,&F$F%*$F$#F%F$F%F%<#-F(6#7%F%,$F/F+F%7%,& F$F%F/F+F%<#-F(6#7%F%F/F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "s1:=eigenvects(A2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G6%7%, $*&\"\"#\"\"\")%'omega0GF)F*F*F*<#-%'vectorG6#7%!\"\"\"\"!F*7%*&,&F)F* *$F)#F*F)F*F*F+F*F*<#-F/6#7%F**&,&F5F2*&F)F*F+F*F*F*F,!\"#F*7%*&,&F)F* F7F2F*F+F*F*<#-F/6#7%F**&,&FBF2*&F)F*F+F*F*F*F,F@F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "r2:=s1[2][3][1][2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2G*&,&*&,&\"\"#\"\"\"*$F)#F*F)F*F*)%'omega0GF)F*!\" \"*&F)F*F-F*F*F*F.!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s implify(r2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$\"\"##\"\"\"F%!\" \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "r3:=s1[3][3][1][2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r3G*&,&*&,&\"\"#\"\"\"*$F)#F*F)! \"\"F*)%'omega0GF)F*F-*&F)F*F.F*F*F*F/!\"#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "simplify(r3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$ \"\"##\"\"\"F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "8 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }