Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 183 стр.

UptoLike

Составители: 

Рубрика: 

cÈÏËã


ÒÓˮөËÏÈmÒ°Ò亰ÒmãÒÓˮӺä¹¯º°¯ÈÓ°mË
|¹¯ËËãËÓÒË

Íévqoknlntqnu ãÒÓˮө² º¹Ë¯Èº¯ºm
A
Ò
B
ÓÈÏ©mÈË°« º¹Ë¯Èº¯
ººÏÓÈÈËä©®
A
B
°Èm«Ò®}ÈκäªãËäËÓãÒÓˮӺº¹¯º°¯ÈÓ
°mÈ
Λx
m°ººmË°mÒËªãËäËÓ
)
ˆ
(
ˆ
xBA

˺¯ËäÈ

¯ºÒÏmË
ËÓÒËãÒÓˮө²º¹Ë¯Èº¯ºm«mã«Ë°«ãÒÓˮөäº¹Ë¯Èº¯ºä
ã«}ºº¯ºº°¹¯ÈmËãÒm©°ººÓºËÓÒ«
(

)(

)
;
(

)

;
(

)

.
ABC ABC
AB C AB AC
ABCACBC
=
+= +
+=+
iº}ÈÏÈËã°mº
iº}ÈÎËä mÓÈÈãË ãÒÓˮӺ° ¹¯ºÒÏmËËÓÒ« ãÒÓˮө² º¹Ë¯Èº¯ºm iË®°mÒ
ËãÓº

()
(

)
(
)
(
)(

)(

)
AB x y A Bx By A Bx A By AB x AB y
αβ α β α β α β
+= + = + = +

¯ºm˯Òä˹˯°ºËÈËãÓ©®ÏÈ}ºÓã«¹¯ºÒÏmËËÓÒ«ãÒÓˮө²º¹Ë¯Èº¯ºm
jäËËä
(
(

))
(

)
(
(
))ABC x ABCx ABCx==

Óº°¯º®°º¯ºÓ©
((

)
)

(
)
(
(
))
A B C x AB Cx A B Cx
==

ºÒ¯ËºmÈ㺰 ¹º}ÈÏÈ |°ÈãÓ©Ë m˯ÎËÓÒ« ˺¯Ëä© ¹¯ºm˯«°«
ÈÓÈãºÒÓº
˺¯ËäÈº}ÈÏÈÓÈ
~ÈäËÈÓÒË
{ºËä°ãÈË ¹¯ºÒÏmËËÓÒËãÒÓˮө²º¹Ë¯Èº¯ºm ÓË ºãÈÈË wnén
xzjtvkv·tuxkvpxzkvuÒãÒÒÓÈË ºmº¯«vwnéjzvé tnrvuuyzqéy
ízº˰
 
AB BA

|¹¯ËËãËÓÒË

|¹Ë¯Èº¯
 
AB BA
ÓÈÏ©mÈË°«rvuuyzjzvévuº¹Ë¯Èº¯ºm
A
Ò
B

zºääÈº¯}ºääÒ¯Ò²º¹Ë¯Èº¯ºm˰ÓãËmº®º¹Ë¯Èº¯
cÈÏËã 
ÒÓˮөËÏÈmÒ°Ò亰ˆÒmãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmË



    |¹¯ËËãËÓÒË           Íévqoknlntqnu ãÒÓˮө² º¹Ë¯Èˆº¯ºm A  Ò B  ÓÈÏ©mÈˈ°« º¹Ë¯Èˆº¯
    
                           º­ºÏÓÈÈËä©® A B °ˆÈm«Ò®}Èκ䂪ãËäËӈ‚ãÒÓˮӺº¹¯º°ˆ¯ÈÓ
                           °ˆmÈ x ∈ Λ m°ººˆmˈ°ˆmÒ˪ãËäËӈ Aˆ ( Bˆ x ) 
             
             
             
    ‘˺¯ËäÈ               ¯ºÒÏmËËÓÒËãÒÓˮө²º¹Ë¯Èˆº¯ºm«mã«Ëˆ°«ãÒÓˮө亹˯Ȉº¯ºä
                    ã«}ºˆº¯ºº°¹¯ÈmËãÒm©°ººˆÓºËÓÒ«
                           
                                                                       A ( BC
                                                                               ) = ( AB
                                                                                         )C ;
                                                                       A ( B + C ) = AB
                                                                                           + AC
                                                                                                 ;
                                                                       ( A + B )C = AC  + BC
                                                                                                .
           
     iº}ÈÏȈËã°ˆmº
      
      
         iº}ÈÎËä mÓÈÈãË ãÒÓˮӺ°ˆ  ¹¯ºÒÏmËËÓÒ« ãÒÓˮө² º¹Ë¯Èˆº¯ºm iË®°ˆmÒ
         ˆËã Óº
         
                         (α x + β y ) = A (α Bx
                       AB                        + β By
                                                       ) = α A ( Bx
                                                                    ) + β A ( By
                                                                                 ) = α ( AB
                                                                                            ) x + β ( AB
                                                                                                          ) y 
           
           ¯ºm˯ÒäˆË¹Ë¯ °ºˈȈËã Ó©®ÏÈ}ºÓ㫹¯ºÒÏmËËÓÒ«ãÒÓˮө²º¹Ë¯Èˆº¯ºm
           jäËËä
           
                                                       ( A ( BC
                                                                )) x = A ( BCx
                                                                                ) = A ( B (Cx
                                                                                                )) 
           Óº°¯‚º®°ˆº¯ºÓ©
                                                        (( A B )C ) x = AB
                                                                             (Cx
                                                                                 ) = A ( B (Cx
                                                                                                )) 
           
           ˆº Ò ˆ¯Ë­ºmÈ㺰  ¹º}ÈÏȈ  |°ˆÈã Ó©Ë ‚ˆm˯ÎËÓÒ« ˆËº¯Ëä© ¹¯ºm˯« ˆ°«
           ÈÓÈãºÒÓº
      
      
      ‘˺¯ËäȺ}ÈÏÈÓÈ
             
             
             
    ~ÈäËÈÓÒË            { º­Ëä °ã‚ÈË ¹¯ºÒÏmËËÓÒË ãÒÓˮө² º¹Ë¯Èˆº¯ºm ÓË º­ãÈÈˈ wnén
                           xzjtvkv·t€u xkvpxzkvu ÒãÒ ÒÓÈË ºmº¯« vwnéjzvé€ tn rvuuyzqéy
                           íz ˆº˰ˆ  A B ≠ B A 
             
             
             
    |¹¯ËËãËÓÒË           |¹Ë¯Èˆº¯ A B − B A ÓÈÏ©mÈˈ°«rvuuyzjzvévuº¹Ë¯Èˆº¯ºm A Ò B 
    
             
             
             zºä䂈Ȉº¯}ºä䂈ү‚ Ò²º¹Ë¯Èˆº¯ºm˰ˆ ӂãËmº®º¹Ë¯Èˆº¯