11transformations.usuelles

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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

    ( ) .