{VERSION 5 0 "IBM INTEL NT" "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 "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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 }} {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 0 137 "i s_unitary:=U -> equal(htranspose(U),inverse(U));\nis_hermitian:=H->equ al(htranspose(H),H);\nis_posDefinite:=P->definite(P,'positive_def');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+is_unitaryGf*6#%\"UG6\"6$%)operat orG%&arrowGF(-%&equalG6$-%+htransposeG6#9$-%(inverseGF1F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%-is_hermitianGf*6#%\"HG6\"6$%)operat orG%&arrowGF(-%&equalG6$-%+htransposeG6#9$F2F(F(F(" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%/is_posDefiniteGf*6#%\"PG6\"6$%)operatorG%&arrowGF( -%)definiteG6$9$.%-positive_defGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "### Matrix A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "A := linalg[fibonacci](5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"AG-%'matrixG6#7*7*\"\"\"F*F*F*F*F*F*F*7*F*\"\"!F*F*F,F*F,F*7*F*F*F,F *F*F*F*F,7*F*F*F*F,F,F*F*F*7*F*F,F*F,F,F*F,F*7*F*F*F*F*F*F,F,F,7*F*F,F *F*F,F,F,F,7*F*F*F,F*F*F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ASigma := evalf(Svd(A,AU,AV));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%'ASigmaG-%'vectorG6#7*$\"+'R0xX&!\"*$\"+iN@9CF+$\"+,O'3z\"F+$\"+++ ++5F+$\"+Mlg&[(!#5$\"+k<^ " 0 "" {MPLTEXT 1 0 10 "evalm(AU);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$!+6!z/0&!#5$!+hdQ/A!#D$\"+da**GCF*$!+y&G)Q^F-$! +>-DK>!#6$\"+s7@irF*$!+fr`\"3&F-$!+:$zU:%F*7*$!+PwkxMF*$\"+1R`NNF*$!+8 Kl*R$F*$\"+++++]F*$!+s(p.>\"F*$\"+_;TT9F*F>$\"+x>b!y%F*7*$!+ofyQQF*$!+ 1R`NNF*$\"+)3sz3%F*FB$\"+-h4MDF*$!+-&ex0$F*FM$\"+Ag`n;F*7*FKF>FO$!++++ +]F*FQFSF>FU7*$!+(oxUx#F*FB$!+C7(p6\"F*$\"+(R5\"R;F-$!+&Qhcd%F*$!+E%>( )R$F*FX$!+l$yq#HF*7*F " 0 "" {MPLTEXT 1 0 10 " evalm(AV);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$!+6!z/0 &!#5$\"+wtJ`i!#E$!+da**GCF*$\"+sZ%\\K#!#D$!+>-DK>!#6$!+s7@irF*$\"+l0>' y&F-$!+:$zU:%F*7*$!+PwkxMF*$!+1R`NNF*$\"+8Kl*R$F*$!+++++]F*$!+s(p.>\"F *$!+_;TT9F*$\"+1R`NNF*$\"+x>b!y%F*7*$!+ofyQQF*FI$!+)3sz3%F*FC$\"+-h4MD F*$\"+-&ex0$F*F?$\"+Ag`n;F*7*FNF?FP$\"+++++]F*FRFTFIFV7*$!+(oxUx#F*FC$ \"+C7(p6\"F*$!+i=&Hm*F-$!+&Qhcd%F*$\"+E%>()R$F*FC$!+l$yq#HF*7*F=FIFAFY FEFGF?FK7*$!+a\\7KBF*$!+BUE1rF-$\"+4.p@fF*$!+bo5i%)F-$\"+#[aC^'F*$\"+; T\"ol\"F*$!+[jj_EF2$!+)*H^'y$F*7*FfnFYFhn$!+^4ZXFF2F\\oF^oFYF`o" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "is_unitary(A);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "is_hermitian(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "is_posDefinite(A);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'mat rixG6#7*7*\"\"!!\"\"F(F(\"\"\"F)F*F*7*F)F*F(F*F)F*F)F(7*F(F(F(F(F(F*F( F)7*F(F*F(F(F)F(F(F(7*F*F)F(F)F*F(F(F(7*F)F*F*F(F(F*F)F)7*F*F)F(F(F(F) F*F(7*F*F(F)F(F(F)F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "co nd(A);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#[" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "### \+ Matrix B" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "B := linalg[hil bert](8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'matrixG6#7*7*\" \"\"#F*\"\"##F*\"\"$#F*\"\"%#F*\"\"&#F*\"\"'#F*\"\"(#F*\"\")7*F+F-F/F1 F3F5F7#F*\"\"*7*F-F/F1F3F5F7F:#F*\"#57*F/F1F3F5F7F:F=#F*\"#67*F1F3F5F7 F:F=F@#F*\"#77*F3F5F7F:F=F@FC#F*\"#87*F5F7F:F=F@FCFF#F*\"#97*F7F:F=F@F CFFFI#F*\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "BSigma := e valf(Svd(B,BU,BV));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'BSigmaG-%'ve ctorG6#7*$\"+(**Qfp\"!\"*$\"+8@D\")H!#5$\"+dVG@E!#6$\"+<\")on9!#7$\"+3 E%pV&!#9$\"+bXK%H\"!#:$\"+LUs*z\"!#<$\"+$\\N+5\"!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(BU);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$!+%p8F?(!#5$\"+.%R[H'F*$\"+4DZvFF*$!+XIq^')!#6$ \"+eubl?F1$!+&[J1\"Q!#7$\"+u&p\"Q_!#8$\"+%oHdr%!#97*$!+a,EDVF*$!+;&3nD \"F*$!+uZG\\kF*$\"+0>Q,bF*$!+1*e7m#F*$\"+&H^\"z&)F1$!+3$G2)=F1$!+_D*\\ `#F67*$!+kkV)=$F*$!+4->kGF*$!+=`]^LF*$!+c,aiLF*$\"+EzlSiF*$!+?L%z=%F*$ \"+jw&*z:F*$\"+3bx$F1$\"+r)prz&F*$!+:tDX\\F*$!++\\())z\"F*7*$!+6&>'Q@F*$!+`H%4K$F*$ \"+Q7CS9F*$!+$>'\\cFF*$!+)QXQ>%F*$\"+4@-K7F*$\"+&p#zkcF*$\"+g%o1&[F*7* $!+*)y>X=F*$!+l'*RNKF*$\"+Q0jGFF*$!+O1sf#3%F*$\"+x\">\"HGF*$!+S_&HQ\"F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalm(BV);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7*$!+%p8F?(!#5$\"+.%R[H'F*$\"+4DZvFF*$ !+XIq^')!#6$\"+eubl?F1$!+&[J1\"Q!#7$\"+u&p\"Q_!#8$\"+s'Hdr%!#97*$!+a,E DVF*$!+;&3nD\"F*$!+uZG\\kF*$\"+0>Q,bF*$!+1*e7m#F*$\"+&H^\"z&)F1$!+3$G2 )=F1$!+[D*\\`#F67*$!+kkV)=$F*$!+4->kGF*$!+=`]^LF*$!+c,aiLF*$\"+EzlSiF* $!+?L%z=%F*$\"+jw&*z:F*$\"+0bx$F1$\"+r)prz&F*$!+:tDX\\F*$!+**[())z\"F*7*$!+6&>'Q@F*$ !+`H%4K$F*$\"+Q7CS9F*$!+$>'\\cFF*$!+)QXQ>%F*$\"+4@-K7F*$\"+'p#zkcF*$\" +f%o1&[F*7*$!+*)y>X=F*$!+l'*RNKF*$\"+Q0jGFF*$!+O1sf#3%F*$\"+w\">\"HGF*$!+S_&HQ \"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "is_unitary(B);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "is_hermitian(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% %trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "is_posDefinite(B) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'matrixG6#7*7*\"#k!%;?\"&g,#!&+C*\"'g#>!&![^7*F)\"&sY)!' gD&*\"(gpl%!)+Ck6\")_vc:!)%e%f5\"(!)G)G7*F*F2\")?2V6!)+?@e\"*+!)o\\\"! *?TK/#\"*?6ET\"!)!))=*Q7*F+F3F:\"*++#\\I!*+]T+)\"++)3*46!*gh$px\"*+g@; #7*F,F4F;FA\"+++WM@!+gPv'*H\"++o\"*=@!*+Sf%f7*F-F5FFDFIFMFP\"*g$zm<" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "cond(B);" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\",&4\"zsQ$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "23" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }