{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 4 0 34 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 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "restart; with(linalg ):E3:=band([1],3):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protec ted names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "A:=matrix(3,2,[-198,63,-24,- 132,176,136]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7% 7$!$)>\"#j7$!#C!$K\"7$\"$w\"\"$O\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "c1:=col(A,1);\nbeta:=norm(c1,2);\nc1[1]:=c1[1]-beta: \nprint(c1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c1G-%'vectorG6#7%!$ )>!#C\"$w\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG\"$m#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%!$k%!#C\"$w\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "lambda:=norm(c1,2):print(lambda,eva lf(lambda));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*&\"\")\"\"\"\"%dQ#F &\"\"#F&$\"+=+Qo\\!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "v :=(evalm(c1/lambda));evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" vG-%'vectorG6#7%,$*(\"\"#\"\"\"\"$L\"!\"\"\"%dQ#F,F+F.,$*(\"\"$F,F/F.F /F0F.,$*(\"#AF,F/F.F/F0F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vector G6#7%$!+!=g!R$*!#5$!+r$[0$[!#6$\"+R@SUNF)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 58 "H1:=(evalm(E3 - 2*v &* transpose(v))): print(H1,eva lf(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'matrixG6#7%7%#!#**\"$L\" #!#7F*#\"#))F*7%F+#\"%RQ\"%dQ#\"$K\"F27%F-F3#\"%*)GF2-F$6#7%7%$!+B!4OW (!#5$!+\"RcD-*!#6$\"+`8a;mF>7%F?$\"+0;L`**F>$\"+w*[BU$FA7%FBFG$\"+=uF! \\(F>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A1:=evalm(H1 &* A) ;#evalf(%);" }}{PAGEBK }{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G-%'matrixG6#7%7$\"$m#\"#b7$\"\"!#!%SQ\"#H7$F -#\"%KSF0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "c2:=col(A1,2): c2[1]:=0:\nbeta:=norm(c2,2):print(c2,beta); \nc2[2]:=c2[2]-beta: print (evalm(c2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'vectorG6#7%\"\"!#!% SQ\"#H#\"%KSF*\"$#>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7% \"\"!#!%3%*\"#H#\"%KSF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " lambda:=norm(c2,2): print(lambda,evalf(lambda));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "v:=(evalm(c2/lambda)): evalf(%);\nH2:=(evalm(E3 - 2*v &* transpose(v))): print(H2, evalf(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*(\"%W8\"\"\"\"#H!\"\"\"#e#F&\"\"#F&$\"+;p^HN!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"\"!F($!+-.X\">*!#5$\"+')H>RRF+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'matrixG6#7%7%\"\"\"\"\"!F)7%F)# !#?\"#H#\"#@F-7%F)F.#\"#?F--F$6#7%7%$F(F)$F)F)F87%F8$!+C " 0 "" {MPLTEXT 1 0 31 "A2:=evalm(H2 &* A1); #evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #A2G-%'matrixG6#7%7$\"$m#\"#b7$\"\"!\"$#>7$F-F-" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "Q:=evalm(H1&*H2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG-%'matrixG6#7%7%#!#**\"$L\"#\"#sF,#\"#_F,7%#!#7F, #!#))F,#\"#**F,7%#\"#))F,#\"#pF,F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }