Tranformaciones lineales
& ! ! !" ' "# ! ! !" "+ $ " "#- '" ! "
!
! "
" ! "#! $ & ' !" " " ( )!$ ' !" " " ($ &) ! " " & $ ! ! " $ $ "
!
" " " %
"
" ! " "
%" $ " !*
" , ! ! * " !" * '"
" ' " ". ! " "$ ,
# ! ( ! " & !" $/ " "
"
0, 3!.
! + ", " 2 "-"4( ' 5 * / / - ) !" , !" ' !" $ -" " $ -" !" , 6, 1 0 " ! %" $ 1 # $ * ! " 6&7 #" ! ! !" ' !" " " ' $ %" $ " " !( " $/ " " $ 2* )! !% " " 7, 1 8 "5 ' " " " " $ "&* # . !" "$ " ! " " ! , "$" & : $" :" !5 # ! !, ! (: &' 4* # 5 " !5 # ! ! 5 " $" "$" $ " ! ( "
"
1
"$ ' 3 ' & "#
" " " $ " $ ! ! & $# !!" !" * ! " " '
! ! 4& 2
" " ! ( ! $ %" $ " ! ! & , ! )! $ ! 1 7 ! & ( $/ " ! ! !" ' !" " " $ " ! " "#! $ ! , "# " " + ! " !" ! 5" " ! ! $ "9 "#! $ ( :
! " " - " % " " - " % " .% 3 "$ " ! "$ " with(), "! % ! * !!5 ! , 5 ! 1 ;
.% " " *
> restart; with(linalg):
Warning, the protected names norm and trace have been redefined and unprotected
" ( ! " * >
$" * * ! !5 " ! ! $ "9 ! * , " " $ : % ' 5 "
" $ "
" !" "$ " * * . ' $" ) ! !5 # ! ! & - $" ! !5 ! " ! & !
,
#$ %
%
&
'()
vector() * " $" $ ! !
' " $ ! " ! " 5 %" $ ; > restart: with(linalg): u:=vector([1,2,3,4]);Warning, the protected names norm and trace have been redefined and unprotected
;< = 0( 6( 7( 8 > " ' " vector() ! 5 > v:=vector(5); " * % $" ' " % ' "
8
&" "$#
,
$
$ !
!
;< " 5 / "
?
&3 0 ,, ?( = > 4 $" ! "$# ', . " $" '( ' $"
"
?
&!
' " 5 / > evalm(v);
$ % ' > w1:=[1,2,3,4,5,6]; "
= 0( 6( ! & ! %
7(
8(
?>
!"
$
"$"
!
;< = 0( 6( 7( 8(?( @ > ! " "$" $ 2 % ! " "! $ > w2:=matrix(1,3,[a,b,c]); w3:=matrix(3,1,[d,e,f]); ;< = ;< $ :" "$ " ! !2 ! " " !" ' " " ' " ! ( " " ! $" "!" " !" " " $ " ( ' $" "!" !" " " $ $ #! ( " !" * "!" "$ $" !" "$ " basis() & dotprod() 3 )! $" !" $ ! $" " " !& ! 5 4, ! "$ 5 , " *+ #, ,$$$$, * "# -. + # A'0('6(,,,(' B # $ " ! " "' ' " + & !" >
!
" !* ='0('6(,,,(' >(
! ! "$ " */ #, ,$$$$, 0., >B1:=basis({vector([1,1,1]),vector([1,1,0]),vector([2,2,1]),ve ctor([1,0,0])}); ;< A = 0( 0( 0 >( = 0( 0( C >( = 0( C( C > B > B2:=basis([vector([1,1,1]),vector([1,1,0]),vector([2,2,1]),ve ctor([1,0,0])]); ! "$ ;< = = 0( 0( 0 >( = 0( 0( C >( = 0( C( C > > " dotproduct(v,w) "# ! " " ! !" ' " '&D ! "
' " ! !. " " ! " " ! ! E'(DF( * 3 "$" ' $" 4 % "$" ! $ !" " " ! "$ " ' "( ' F:= proc(x) local y;y:=evalm(x); ! " ' = @( J8 > % " * !" ' !" !5 " "#! $ ! % % % % " ' " ! " $ * !" ' !" % . ! 5 $" "; " ' " " ' " , " ! "$ " proc ' " , . ( ( 4→= + + (− − > % "$"
" $ !
vector([y[1]+y[2]+y[3],-y[1]-y[3]]); end; ;< 3 4 K ;< ' !$3 4 K ' > F([1,2,3]); "# & * & " ' " ! ; > u:=vector(3); ;< > F(u); = > v:=vector(3); ;< > F(v); = > F(u)+F(v); = > F(u+v); = ' % * !"
0 0 0 0
" 3 = = 0 > + = 6 > + = 7>( − = 0 > − = 7 > > 4 = @( J8 >
&
!
!
# $" "$ "# )$ " !(
7
* )$ "
(' " ' , !,
"
7
" ! ! "
&
% * $" *
&3 0 ,, 7( = > 4
6
+
+
7(
−
0
−
7>
&3 0 ,, 7( = > 4
6
+ −
+
7>
7(
−
0
−
7>
+ +
6
+ +
7(
− +
0
+= +
0
+
6
+
7(
−
0
−
7>
0
6
6
+ "
7
7(
−
0−
0
−
7
− !2
7>
" )! $" ' " ' ! ! % !!" 4; > equal(F(u)+F(v),F(u+v)); > F(a*u); = > a*F(u);
0
5 !
" $"
! "$
" "
3"
+
6
+
7(
−
0
−
7>
= 0 + 6 + 7( − 0 − 7 > ' % * !" " )! $" ' " " 5 ! " $" : ' ! ! % !!" 3" ! 2 ! "$ " 4; > simplify(evalm(F(a*u)-a*F(u))); = C( C > ; ! %! ( $ 2 JJF ' $ ( ! * ( & % " 1 ! !& !" " % 1 ! " ! # "!! " !( ! % 1 (!$ 5 "" ! , " ! "" & ! 1 ! " !'
!" $ $" *
"#
! " ! "
& ( 1 " ! % " $ 2 ! $ " 4 ! # 1 ( ( " ! $ 2
"! $ !* "# $ ! ! ( " "' ! $ 2 "
" "' " " ! ' " "! $ 32 "! $
&
!" '
"
*
"
$ 5
!"
"
"
'
"
! #
1
, !
! "$ " 3 */4*3./#0,4*3./ 0,$$$,4*3./ 00,/3/#0,3/ 0,$$$,3/ 00. " $ $ 2 ; > A:= genmatrix([F(x)[1],F(x)[2]],[x[1],x[2],x[3]]); ;< " $" '
7...
Regístrate para leer el documento completo.