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7/25/2019 11transformations.usuelles
1/2
.
(I A(
k .'M k
) , )h k M( )P'MM
"'M k M =
.B(
MN'M'N
h 1k
' 'M N k MN=
.
C( h k.
(1( ) 'h M M='M k M =
2) ( ) 'h M M=( ) 'h N N=
' 'M N k MN=
(3(a( )h = ) )h
(b( )h M M=M =
) h(
4) ( ) 'h M M=M'M.
(5(a :
){ }G , ), ( , )A B G'
{ }( ', ), ( ', )A B (b :
I[ ]A BI'[ ]' 'A B
(c :
A B CD=
' ' ' 'A B C D=
(d 3 : ABC .A'B'C'
(6 .
) ) 'h A A=( ) 'h B B=' 'A B k A B=
(7 ' ' 'BA C B A C
=
(a (8[ ]ABh[ ]' 'A B
(b( )ABh( ' ')A B.
(c ) )D ( ')D( )D.
(d ) )Dh
AB( )D( ) ( ' ')h D A B=
)A )h D 'A
( )D) .( ) 'h A A=(
(e( )D
) ) ( )h D D=
.( ) )D. (
)9) , )C O rh'( ', )C O k r .
' ( )O h O=.
(10(aEF .( ) ( ) ( )h E F h E h F =
(b M E F ) ) ( ) ( )h M h E h F
(11 :
.
12( .
) , , )O i j
.
a(1:h (1,2)2k =. h :
( , )M x y( ', ')M x y( ) 'h M M=
'x'yxy.
( ) 'h M M=' 2M M =
'( ' 1, ' 2)M x y
2 (2 2,2 4)M x y
' 1 2 2
' 2 2 4
x x
y y
=
=
' 2 1
' 2 2
x x
y y
=
=
:h' 2 1
:' 2 2
x xh
y y
=
=
: hA xy A ( )h A.
b(2.
:' 3 2
:
' 3 4
x x
y y
= +
=
'
'
x x
y y
=
=
3 2
3 4
x x
y y
+ =
=
1
2
x
y
=
= f
( 1, 2) .
( , )M x y( ', ')M x y( ) 'h M M=
' 3 2
' 3 4
x x
y y
= +
= .'( 1, ' 2)M x y +
'(3 2 1,3 4 2)M x y + + '(3 3,3 6)M x y +
3 (3 3,3 6)M x y +
' 3M M =
( 1, 2) 3k =.
)13 .(a h. AB
A'B'.( ) 'h A A= AA'
( ')AA .( ) 'h B B= 'BB
( ')BB ( ')AA
( ')BB
7/25/2019 11transformations.usuelles
2/2
(b hk:(* AA'.
( ) 'h A A= 'A k A =
'A
A
'A A =
k =
'A k M = 'A
kM
=
.
(* ABA'B'.
' 'A B k AB= .
(c '[ ]'I 'A B IAB
( ) 'h A A=( ) 'h B B=( ) 'h I I=
(5b.I[ ]AB '[ ]'I 'A B.
(d IJ
( , )( )kh I J =.
(e M :
(*'M k M =
*) M[ ]AB(5b).
A*) M AB=
(5c).
(* M (10).
) M E F ) ) ( ) ( )h M h E h F (
(* .
(II A(.'M
S
M( )P'M
"'M M =
[ ]'MM.M
B(MN'M'N
S
' 'M N MN=
.
C(
k1- (6)(9).
(6 .
) ) 'h A A=
( ) 'h B B=
' 'A B AB=
)9) , )C O rS
'( ', )C O r .' ( )O S O
=.
(a( ) 'S M M
=[ ]'MM.
(b( ) 'S M M
=( ) 'S N N
=
' 'M N MN=
.
(III A(.
u
. u
u
'Mut
M( )P'M
"'MM u=
M
B(
MN'M'N
ut ' 'M N MN=
.
C( (1)
(2)(3)(4)(6)(8cde)(9)(12)(13abd):
(6 .
(8e ( )D u
)u
) )D(
( ) ( )ut D D=.
)9) , )C O rut'( ', )C O r .
' ( )uO t O=
.
(a( ) 'ut M M='MM u=
.
(b ( ) 'ut M M=( ) 'ut N N=
' 'M N MN=
.
(III
A(.( ) ( )( )
) )S
M( )P'MM'M
) )[ ]'MM.
B(
:(1)(2)(3)(4)(5(6)(8e)(9)(13abd)
(6 .
(8e(* ( ) ( )D ) ) ( ) ( )t D D =.
)*) ) //( )D ) ) ( ) //( )t D D.
)9) , )C O r( )
S
'( ', )C O r .( )' ( )O S O=.
(a
( )( ) 'S M M
=( ) .[ ]'MM
(b ( ) ( )S M M =( )M
( ) .