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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 30 "Matrices and matrix opera
tions" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=array(1..2,1..3,[]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%&arrayG6%;\"\"\"\"\"#;F)\"\"$7
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%&arrayG6$;\"\"\"\"\"$7\"" }}}
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" {XPPMATH 20 "6#-%'MATRIXG6#7$7%&%\"AG6$\"\"\"F+&F)6$F+\"\"#&F)6$F+\"
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{MPLTEXT 1 0 9 "evalm(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'VECTOR
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" {MPLTEXT 1 0 14 "evalm(B &* A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A:=randmatrix(4,6);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7&7(!#&)!#b!#P!#N\"#(*\"#]7(\"#z
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> " 0 "" {MPLTEXT 1 0 58 "for j from 1 to 6 do A[3,j]:=A[1,j]+2*A[2,j]
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!#b!#P!#N\"#(*\"#]7(\"#z\"#c\"#\\\"#j\"#d!#f7(\"#tF3\"#h\"#\"*\"$6#!#o
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{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "evalf(linsolve(A,vector(4,[0,0,0,0]
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proc(A) if type(A,matrix)=false then 'error' else RETURN(coldim(A)-ran
k(A)) fi; end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(nullityG:6#%\"AG6
\"F(F(@%/-%%typeG6$9$%'matrixG%&falseG.%&errorG-%'RETURNG6#,&-%'coldim
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "R:=rowspace(A);" }}{PARA 11 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7$7&\"\"!F(F(F(F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C:=colspace(A);" }}{PARA 11 
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'7&!#b\"#c\"#d!$X%7&!#P\"#\\\"#h!$c$7&!#N\"#j\"#\"*!$?%7&\"#(*F/\"$6#
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0 "" {MPLTEXT 1 0 24 "T:=array(1..2,1..2,[]): " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 87 "for i from 1 to 2 do for j from 1 to 2 do T[i,
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{XPPMATH 20 "6#-%'MATRIXG6#7$7$\"\"!F(F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "A:=randmatrix(4,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"AG-%'MATRIXG6#7&7&!#`!#h!#B!#P7&\"#J!#M!#U\"#))7&!#w!#l\"#D\"#G7
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lf(Eigenvals(A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$EigG-%'VECTORG
6#7&$\"+<[6ls!\"),&$!++1DtaF+\"\"\"%\"IG$\"+\"z)>xbF+,&F-F/F0$!+\"z)>x
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-lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,\"(0>p\"\"\"\"%'lambdaG
!'xlV*$F&\"\"#!%()>*$F&\"\"$\"#L*$F&\"\"%F%" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 19 "charpoly(A,lambda);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,,\"(0>p\"\"\"\"%'lambdaG!'xlV*$F&\"\"#!%()>*$F&\"\"$\"#L*$F&\"
\"%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "The eigenvalues are zero
s of the characteristic polynomial, however" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 63 "for i from 1 to 4 do subs(lambda=Eig[i],charpoly(A
,lambda)) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#5!\"#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$%\"IG$!#:!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%\"IG$\"#:!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
'r<9!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Eig:=evalf(Eige
nvals(A),20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "for i from
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1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"IG$!
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{PARA 11 "" 1 "" {XPPMATH 20 "6#$!%)\\#!\"(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 29 "Eig:=evalf(Eigenvals(A),100):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 63 "for i from 1 to 4 do subs(lambda=Eig[i],char
poly(A,lambda)) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$%\"IG$!\"\"!\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%\"IG$\"\"\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
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