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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Matrices in Maple." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "To load t
he functions on linear algebra in Maple type:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "with(linalg);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 134 "linalg is a Maple package. See ?index,packages for a list of o
ther packages you can load with with. You can enter a matrix as follow
s:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "matrix(2,2,[ [1,2], [
3,4] ]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "matrix(2,3,[ [1
,2,3],[4,5,6] ]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 303 "So the firs
t argument is the number of rows (called rowdim in Maple), the second \+
is the number of columns (called coldim) and the third is a list of li
sts, where each list represents a row. Since the first two arguments g
ive the dimensions of the matrix, you can also skip the brackets of th
e row lists." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "matrix(2,3,
[ 1,2,3,4,5,6 ]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "matrix
(2,3,[ seq(i,i=1..6) ]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Conca
tenation of names in Maple V release 5 is done by the dot \".\"  In Ma
ple x.5 stands for x5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "s
eq(x.i,i=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "N:=4;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "A:=matrix(N,N,[ seq(seq(x.
i^j,j=0..N-1),i=0..N-1) ]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
2 "A;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(A);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "Matrices have some special status
 in Maple. For one thing, just typing A; doesn't display the matrix, y
ou'll have to use print(A) or op(A)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 6 "op(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "de
t(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "You may remember from linear alge
bra that A is a Vandermonde matrix, and that it's determinant factors \+
as you see here." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "A:=matr
ix(3,3,[ seq(i^2,i=0..8) ]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "det(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "inverse(A);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalm( A^(-1) );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "B:=%;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "multiply(A,B);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "evalm( A &* B);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
108 "Note that in Maple, the * is always commutative. The non-commutat
ive matrix multiplication is denoted by &*." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "evalm(A^3+72*x*B);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "charpoly(A,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "subs(x=A,%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eval
m(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm(lambda - A);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "det(%);" }}}{EXCHG 
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