Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 39 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏ Ëã
43
¯ºÒÏmËËÓÒ«mË}º¯ºm

°
p°ãÒmË}º¯äÓºÎÒÓÈmËË°mËÓÓºËÒ°ãºº˺¹¯ºË}Ò«È}ÎË
äÓºÎÒ°«ÓÈªºÒ°ãº
Pr ( ) Pr
ll
aa
ΛΛ
λλ
→→
=

~ÈäËÒäº°mº®°mÈ°Ò°äºÎÓººËÒÓÒm°ãËËËm˯ÎËÓÒË
¯ºË}Ò« ãÒÓˮӺ® }ºäÒÓÈÒÒ mË}º¯ºm ¯ÈmÓÈ º® ÎË ãÒÓˮӺ®
}ºäÒÓÈÒÒ¹¯ºË}Ò®
Pr ( ) Pr Pr
lll
aa a a
ΛΛΛ
λλ λ λ
11 2 2 1 1 2 2
→→ → →
+= +

v¹¯ÈmËãÒmº°°mº®°m°Ò°m©Ë}ÈËÒÏº¹¯ËËãËÓÒ«º¹Ë¯ÈÒÒº¯ººÓÈã
Óºº¹¯ºË}Ò¯ºmÈÓÒ«Ò¹¯ÈmÒãË®°mÒ«°mË}º¯ÈäÒ
vmº®°mÈÒ°ãËÓÓ©²ÏÓÈËÓÒ®º¯ººÓÈãÓ©²¹¯ºË}Ò®
°
ý ý ý
lll
aa a a
()
12 1 2
→→ → →
+= +

°
ý ý
ll
aa
λλ
→→
=

jãÒºËÒÓ««°Ò°
ý ý ý
lll
aa a a
()
λλ λ λ
11 2 2 1 1 2 2
→→ → →
+= +

|äËÒä º ªÒ ¯ÈmËÓ°mÈ °ãË ÒÏ °mº®°m º¯ººÓÈãÓ©² ¹¯ºË}Ò® Ò
°mº®°m}ºº¯ÒÓÈmË}º¯ºm
v}È㫯ӺË¹¯ºÒÏmËËÓÒËmË}º¯ºmÒ˺°mº®°mÈ
|¹¯ËËãËÓÒË

frjs¹étuwévqoknlntqnu ÓËÓãËm©²mË}º¯ºm
a
→
Ò
b
→
ÓÈÏ©mÈË°«Ò°ãº
¯ÈmÓºË¹¯ºÒÏmËËÓÒãÒÓªÒ²mË}º¯ºmÓÈ}º°ÒÓ°ãÈäËÎ ÓÒäÒ
{°ãÈËË°ãÒ²º« ©ºÒÓÒÏ°ºäÓºÎÒËãË®Ë°Ó ãËmº®mË}º¯°}È 
㫯ӺË¹¯ºÒÏmËËÓÒË°ÒÈË°«¯ÈmÓ©äÓã
c È Ï  Ë ã                                                      43
¯ºÒÏmËËÓÒ«mË}ˆº¯ºm



                      ° p°ãÒmË}ˆº¯‚äÓºÎ҈ ÓÈm˝˰ˆmËÓÓºËҰ㺈ºËº¹¯ºË}Ò«ˆÈ}ÎË
                              ‚äÓºÎ҈°«ÓȪˆºÒ°ãº
                                                                                                 Λ        →                Λ →
                                                                                              Prl (λ a ) = λ Prl a 
                         
                  ~ÈäˈÒ䈺°mº®°ˆmÈ°Ò°äºÎÓºº­žËÒÓ҈ m°ãË‚ ËË‚ˆm˯ÎËÓÒË
                  
                         ¯ºË}Ò« ãÒÓˮӺ® }ºä­ÒÓÈÒÒ mË}ˆº¯ºm ¯ÈmÓÈ ˆº® ÎË ãÒÓˮӺ®
                         }ºä­ÒÓÈÒÒ¹¯ºË}Ò®
                                                                              Λ            →              →                  Λ     →                Λ     →
                                                                             Prl ( λ1 a1 + λ2 a 2 ) = λ1 Prl a1 + λ2 Prl a 2 
       
       v¹¯ÈmËãÒmº°ˆ °mº®°ˆm°Ò°m©ˆË}ÈˈÒϺ¹¯ËËãËÓÒ«º¹Ë¯ÈÒÒº¯ˆººÓÈã 
Óºº¹¯ºË}ˆÒ¯ºmÈÓÒ«Ò¹¯ÈmÒãË®°ˆmÒ«°mË}ˆº¯ÈäÒ
       
       
       
vmº®°ˆmÈÒ°ãËÓÓ©²ÏÓÈËÓÒ®º¯ˆººÓÈãÓ©²¹¯ºË}Ò®
       
                                                                                   →         →                    →                 →
                                                            ° ýl (a1 + a 2 ) = ýl a1 + ýl a 2 
                                    
                                                                                     →                     →
                                                            ° ýl λ a = λ ýl a 
                         
                         
                  jãÒº­žËÒÓ««°Ò°
                  
                                                                                          →              →                          →                        →
                                                                         ýl ( λ1 a1 + λ2 a 2 ) = λ1 ýl a1 + λ2 ýl a 2 
       
       
       |ˆäˈÒä ˆº ªˆÒ ¯ÈmËÓ°ˆmÈ °ãË‚ ˆ ÒÏ °mº®°ˆm º¯ˆººÓÈã Ó©² ¹¯ºË}Ò® Ò
°mº®°ˆm}ºº¯ÒÓȈmË}ˆº¯ºm
       
       
       
       
v}È㫯Ӻ˹¯ºÒÏmËËÓÒËmË}ˆº¯ºmÒ˺°mº®°ˆmÈ
                  
                  
                  
                                                                                                                                                   →          →
    |¹¯ËËãËÓÒË                   frjs¹ét€uwévqoknlntqnuÓËӂãËm©²mË}ˆº¯ºm a Ò b ÓÈÏ©mÈˈ°«Ò°ãº
                            ¯ÈmӺ˹¯ºÒÏmËËÓÒ ãÒÓªˆÒ²mË}ˆº¯ºmÓÈ}º°Òӂ°‚ãÈäË΂ÓÒäÒ
                                   
                                   {°ã‚ÈËË°ãÒ²ºˆ«­©ºÒÓÒÏ°ºäÓºÎ҈Ëãˮ˰ˆ ӂãËmº®mË}ˆº¯°}È
                                   㫯Ӻ˹¯ºÒÏmËËÓÒË°҈Èˈ°«¯ÈmÓ©äӂã 
                  
                  

Страницы