{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" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A: =randmatrix(n,n,entries=rand(-4..4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&!\"%\"\"#F*\"\"\"7&F*!\"\"F.\"\"$7&F+\"\"!F. \"\"%7&F,F2F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "V:=evalm (A&*transpose(A)*1.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%'matr ixG6#7&7&$\"#P\"\"!$\"#@F,$F,F,$\"\"#F,7&F-$\"#FF,$\"\"&F,$!\"$F,7&F/F 5F-$\"\"*F,7&F0F7F:$\"#AF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "ei:=eigenvectors(V);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eiG6&7% $\"+E1Ix;!\")\"\"\"<#-%'vectorG6#7&$\"+m$*GtV!#5$!+D$o9r%F2$!+xCG'e&F2 $\"+$>p6C&F27%$\"+.IwNIF)F*<#-F-6#7&$!*WM2Y'F2$!*_7>#\\F2$\"+$yJ7x'F2$ \"+pvt8tF27%$\"+\">/#*Q&F)F*<#-F-6#7&$\"+jITgxF2$\"+)f!*\\A'F2$\"+B%G8 '**!#6$\"+(H+@#=FU7%$\"*t@t(fF)F*<#-F-6#7&$!+U;5)\\%F2$\"+^:rHiF2$!+j@ D&o%F2$\"+*o3'fVF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "d:=ma trix(n,n,0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "for i to n \+ do d[i,i]:=sqrt(ei[i,1]) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrix G6#7&7&$\"+$3'[&4%!\"*\"\"!F+F+7&F+$\"+gex4bF*F+F+7&F+F+$\"+O*>6M(F*F+ 7&F+F+F+$\"+yh&[W#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R:=[ ]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "for i to n do R:=[op( R),convert(op(ei[i,3]),list)] end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "R:=convert(R,matrix);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'matrixG6#7&7&$\"+m$*GtV!#5$!+D$o9r%F,$!+xCG'e&F,$\"+$>p 6C&F,7&$!*WM2Y'F,$!*_7>#\\F,$\"+$yJ7x'F,$\"+pvt8tF,7&$\"+jITgxF,$\"+)f !*\\A'F,$\"+B%G8'**!#6$\"+(H+@#=FC7&$!+U;5)\\%F,$\"+^:rHiF,$!+j@D&o%F, $\"+*o3'fVF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A:=evalm(tr anspose(R) &* d &* R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'mat rixG6#7&7&$\"+p(p?s&!\"*$\"+h<&\\.#F,$!+T`O)e\"!#5$\"+\\!Qv-$F17&$\"+g <&\\.#F,$\"+BQ,;ZF,$\"+[^1fjF1$!+#=NRi%F17&$!+S`O)e\"F1$\"+X^1fjF1$\"+ P$)z8WF,$\"+b`WV5F,7&$\"+[!Qv-$F1$!+z^$Ri%F1$\"+``WV5F,$\"+YhNRXF," }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalm(A &* transpose(A)); \+ #checking" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&$\"+-+++ P!\")$\"+*******4#F*$!$h#!#5$\"+#*******>!\"*7&F+$\"+#******p#F*$\"+y* *****\\F2$!+&*******HF27&F-F6$\"+6+++@F*$\"+M+++!*F27&F0F8F=$\"+1+++AF *" }}}}{MARK "13" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }