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{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 38 "V \+
:= matrix([[-3,-3],[-1,2],[2,0.3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"VG-%'matrixG6#7%7$!\"$F*7$!\"\"\"\"#7$F-$\"\"$F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "VTV := multiply(transpose(V),V);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$VTVG-%'matrixG6#7$7$\"#9$\"#w!\"\"
7$F+$\"%48!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dete := d
et(VTV);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%deteG$\"&]D\"!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "invA := inverse(VTV);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%invAG-%'matrixG6#7$7$$\"+))y-V5!#5$
!+#*oxbg!#67$F-$\"+\\y`:6F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "B := multiply(V,invA);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%
'matrixG6#7%7$$!+'f]BJ\"!#5$!+z/))H:F,7$$!+mK=aAF,$\"+(Q`m$GF,7$$\"+pC
Q/>F,$!+L-%\\w)!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "P := \+
multiply(B,transpose(V));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'
matrixG6#7%7%$\"+DKpE&)!#5$!+i.TZ<F,$!+O`m$3$F,7%$!+j.TZ<F,$\"+S+\\FzF
,$!+;0PdOF,7%$!+P`m$3$F,F6$\"+Jn\"ea$F," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "multiply(P,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'
matrixG6#7%7%$\"+BKpE&)!#5$!+l.TZ<F*$!+L`m$3$F*7%$!+n.TZ<F*$\"+R+\\FzF
*$!+:0PdOF*7%$!+M`m$3$F*F4$\"+Hn\"ea$F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "V := matrix([[1,0],[0,1],[0,0]]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"VG-%'matrixG6#7%7$\"\"\"\"\"!7$F+F*7$F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "multiply(transpose(V),V);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$\"\"\"\"\"!7$F)F(" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "multiply(V,transpose(V));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"\"\"\"!F)7%F)F(F
)7%F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "S := matrix(3,
1,s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG-%'matrixG6#7%7#-%\"sG6
$\"\"\"F-7#-F+6$\"\"#F-7#-F+6$\"\"$F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 64 "P := multiply(S,inverse(multiply(transpose(S),S)),tra
nspose(S));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7%7%*
&*$)-%\"sG6$\"\"\"F0\"\"#F0F0,(*$F,F0F0*$)-F.6$F1F0F1F0F0*$)-F.6$\"\"$
F0F1F0F0!\"\"*&*&F-F0F6F0F0F2F=*&*&F-F0F:F0F0F2F=7%F>*&*$F5F0F0F2F=*&*
&F6F0F:F0F0F2F=7%F@FE*&*$F9F0F0F2F=" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Id := Matrix(3,3,shape=identity);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#IdG-%'RTABLEG6$\")Kw)R'-%'MATRIXG6#7%7%\"\"\"\"\"!
F/7%F/F.F/7%F/F/F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm
(Id - P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%,&*&*$)-%
\"sG6$\"\"\"F/\"\"#F/F/,(*$F+F/F/*$)-F-6$F0F/F0F/F/*$)-F-6$\"\"$F/F0F/
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/F/F1F<F<F/F/,$*&*&F5F/F9F/F/F1F<F<7%F@FG,&*&*$F8F/F/F1F<F<F/F/" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 
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