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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 38 "Creating Matrices and Ve
ctors in Maple" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 283 26 "Version .8 fo
r Maple V R7." }}}{EXCHG {PARA 256 "" 0 "" {TEXT 257 57 "Load pointers
 to functions in the linear algebra package." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning
, the protected names norm and trace have been redefined and unprotect
ed\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 258 37 "Entering a matrix as a
 list of lists." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "A1 := matrix([ [
1,2,3], [4,5,6], [7,8,9] ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G
-%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"'7%\"\"(\"\")\"\"*" }}
}{EXCHG {PARA 256 "" 0 "" {TEXT 259 37 "Enter a vector - will be viewe
d as a " }{TEXT 260 6 "column" }{TEXT 261 9 "  vector." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "v1 := vector([1, 2, 3]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v1G-%'vectorG6#7%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 262 162 " We could now multiply A1 times v1 by evalm
(A1 &* v1);\nAnother form of the vector call is vector(3,1) producing \+
a column vector of dim 3 with \ninitial  entries 1." }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "v2 := vector(3,1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#v2G-%'vectorG6#7%\"\"\"F)F)" }}}{EXCHG {PARA 256 "" 0 "" 
{TEXT 263 74 "Enter a 2 by 3 matrix with entries taken in row major or
der from the list." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A2 := matrix(
2,3,[x,y,z,w,u,v]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G-%'matrix
G6#7$7%%\"xG%\"yG%\"zG7%%\"wG%\"uG%\"vG" }}}{EXCHG {PARA 256 "" 0 "" 
{TEXT 264 56 "Enter a 2 by 2 matrix with all entries initialized to 0.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "A3 := matrix(2,2,0);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#A3G-%'matrixG6#7$7$\"\"!F*F)" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 265 80 "One can also define a function of row \+
and column indices to initialize a matrix." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "f := (i,j) -> j * x^(i + j);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fGf*6$%\"iG%\"jG6\"6$%)operatorG%&arrowGF)*&9%\"\"
\")%\"xG,&9$F/F.F/F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "A4 := matrix(2,2,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A4G-%'m
atrixG6#7$7$*$)%\"xG\"\"#\"\"\",$*$)F,\"\"$F.F-7$F0,$*$)F,\"\"%F.F-" }
}}{EXCHG {PARA 256 "" 0 "" {TEXT 266 24 "A 1 by 3 matrix; i.e. a " }
{TEXT 267 3 "row" }{TEXT 268 1 " " }{TEXT 269 7 "vector." }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 20 "v3 := matrix(1,3,4);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#v3G-%'matrixG6#7#7%\"\"%F*F*" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT 270 33 " Another form of a column vector." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 26 "v4 := matrix(2,1,[ 5, 6]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#v4G-%'matrixG6#7$7#\"\"&7#\"\"'" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 271 36 "Matrices can be partially specified:" }
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A4 := matrix(2,
3,[[x,y,z]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A4G-%'matrixG6#7$7
%%\"xG%\"yG%\"zG7%&F$6$\"\"#\"\"\"&F$6$F0F0&F$6$F0\"\"$" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 272 24 "And then updated with a " }{TEXT 284 
3 "for" }{TEXT 285 6 " loop." }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "for j from 1 to 3 do\n\011A4[2,j] := x * y^j:\n  od:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "print(A4);" }}{PARA 0 "" 0 "" 
{TEXT 286 65 "Nested loops are also possible to update all entries of \+
a matrix." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7$7%%\"xG%\"yG%\"zG7%*&F(\"\"\"F)F-*&F(F-)F
)\"\"#F-*&F(F-)F)\"\"$F-" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 273 37 "Ma
trices can be stacked horizontally." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "A5 := augment(A2,A4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A5G-%'
matrixG6#7$7(%\"xG%\"yG%\"zGF*F+F,7(%\"wG%\"uG%\"vG*&F*\"\"\"F+F2*&F*F
2)F+\"\"#F2*&F*F2)F+\"\"$F2" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 274 14 
"Or vertically:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "A6 := stackmatrix(A2,v3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
A6G-%'matrixG6#7%7%%\"xG%\"yG%\"zG7%%\"wG%\"uG%\"vG7%\"\"%F2F2" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 275 46 " One can delete a range of rows
 from a matrix." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "delrows(A1,1..2);" }}{PARA 256 "" 0 "" {TEXT 276 27 "
 (Use delcols for columns.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matr
ixG6#7#7%\"\"(\"\")\"\"*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 282 66 " B
lock diagonal or diagonal matrices can also be easily generated." }
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A6 := diag(lamb
da_1, lambda_2);" }}{PARA 256 "" 0 "" {TEXT 277 58 "(These commands ca
n be used with more than two arguments.)" }{MPLTEXT 1 0 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#A6G-%'matrixG6#7$7$%)lambda_1G\"\"!7$F+%)
lambda_2G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A7 := diag(A6,
A6):" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 278 41 " One can create a 5 x \+
5 banded matrix by:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "band([a,b,c]
,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'%\"bG%\"cG\"\"
!F*F*7'%\"aGF(F)F*F*7'F*F,F(F)F*7'F*F*F,F(F)7'F*F*F*F,F(" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 279 65 " A 3 by 3 Jordan block with diagonal e
ntry 5 can be generated by:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Jord
anBlock(5,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%\"\"&
\"\"\"\"\"!7%F*F(F)7%F*F*F(" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 280 59 
"Extract a submatrix using rows 1..3 of A1 and columns 2..3." }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "A8 := submatrix(A1,1..3,2..3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#A8G-%'matrixG6#7%7$\"\"#\"\"$7$\"\"&\"\"'
7$\"\")\"\"*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 281 37 " Extract rows \+
and columns as vectors." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "row(A8,2
); col(A8,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$\"\"&\"
\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"#\"\"&\"\")" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "24 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }