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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "A:=matrix(3,3,[1,1,1,0,-1,3,
-1,3,-1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7%7%\"
\"\"F*F*7%\"\"!!\"\"\"\"$7%F-F.F-" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "x1:=vector([1,0,-1]);" }}{PARA 11 "" 1 "" {XPPMATH 
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20 "6#>%#x2G-%'VECTORG6#7%\"\"\"!\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "x3:=vector([1,3,-1]);" }}{PARA 11 "" 1 "" {XPPMATH 
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" {MPLTEXT 1 0 27 "W:=GramSchmidt([x1,x2,x3]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"WG7%7%\"\"\"\"\"!!\"\"7%\"\"#F)F+7%#F+\"\"$#\"\")F.
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#u1G7%\"\"\"\"\"!!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "u2:=op(2,W);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#u2G7%\"\"#!\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "u3:=op(3,W);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#u3
G7%#\"\"#\"\"$#\"\")F(F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 
"norm(u1,2), norm(u2,2), norm(u3,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
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0 6 "?norm " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "v1:=evalm(u1
/sqrt(2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G-%'VECTORG6#7%,$*$
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{MPLTEXT 1 0 17 " v2:=evalm(u2/3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#v2G-%'VECTORG6#7%#\"\"#\"\"$#!\"\"F+F)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 26 "v3:=evalm(u3/(2*sqrt(2)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v3G-%'VECTORG6#7%,$*$\"\"##\"\"\"F+#F-\"\"',$F*#F+\"
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}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "multiply(transpose(Q),Q);
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(F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "R:=multiply(
transpose(Q),A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG-%'MATRIXG6#
7%7%*$\"\"##\"\"\"F+,$F*!\"\"F*7%\"\"!\"\"$F/7%F1F1,$F*F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalm(A), multiply(Q,R);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$-%'MATRIXG6#7%7%\"\"\"F(F(7%\"\"!!\"\"\"\"$7
%F+F,F+F#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 34 "The \"one command\" QR decomposition" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "R1:=QRdecomp(A,Q='Q1');" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#R1G-%'MATRIXG6#7%7%*$\"\"##\"\"\"F+,$F*!\"\"F*7%\"\"!\"\"$F/7
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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%,$*$\"\"##\"\"\"F*F+
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "A:=matrix(3,5,[1,2,3,4,5,5,4,3,2,1,
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\"\"\"\"\"#\"\"$\"\"%\"\"&7'F.F-F,F+F*7'F+F-F+\"\"(\"\")" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "R2:=QRdecomp(A,Q='Q2');" }}{PARA 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(Q);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'MATRIXG6#7%7%,$*$\"\"##\"\"\"F*F+#F*\"\"$,$F)#F,\"\"
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{MPLTEXT 1 0 16 "B:=transpose(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"BG-%'MATRIXG6#7'7%\"\"\"\"\"&\"\"#7%F,\"\"%F.7%\"\"$F0F,7%F.F,\"\"(
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$\"#b#\"\"\"\"\"#,$F*#\"\"(\"#6,$F*#\"#%)F+7%\"\"!,$*$\"$5\"F,#\"\"'F2
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{XPPMATH 20 "6$-%'MATRIXG6#7'7',$*$\"#b#\"\"\"\"\"##F,F*,$*$\"$5\"F+#
\"\"%F*,$*$\"$q)F+#F-\"$N%,$*$\"&5A(F+#F,F8\"\"!7',$F)#F-F*,$F0#F,\"#A
,$F5#\"\"$\"$!H,$F:#!#K\"&N?\",$*$\"$m\"F+#F-\"#$)7',$F)#FFF*,$F0F.,$F
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#!\"&FP7',$F)#F,\"#6,$F0#!\"#F*F4,$F:#\"#zF;,$FM#\"\"(FN-F$6#7'7%F),$F
)#F_pFfo,$F)#\"#%)F*7%F=,$F0#\"\"'Ffo,$F0#F,F17%F=F=,$F5#F,\"#57%F=F=F
=Fcq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "multiply(transpose(
Q4),Q4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7'7'\"\"\"\"\"
!F)F)F)7'F)F(F)F)F)7'F)F)F(F)F)7'F)F)F)F(F)7'F)F)F)F)F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalm(Q), evalm(R);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$-%'MATRIXG6#7%7%,$*$\"\"##\"\"\"F*F+#F*\"\"$,$F)#F
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%F3F3,$F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "b:=vector([1
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\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "multiply(tran
spose(Q),b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTORG6#7%,$*$\"\"
##\"\"\"F)!\"\"F),$F(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{MARK "30 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }