Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 185 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 

cÈÏËã


ÒÓˮөËÏÈmÒ°Ò亰ÒmãÒÓˮӺä¹¯º°¯ÈÓ°mË
|¹¯ËËãËÓÒË

|¹Ë¯Èº¯
B
ÓÈÏ©mÈË°« viéjztu º¹Ë¯Èº¯
A
Ò ººÏÓÈÈË°«
A
−1

Ë°ãÒ

AB BA E
==

¯Òä˯

{ ãÒÓˮӺä ¹¯º°¯ÈÓ°mË ÁÓ}Ò®
f
()
τ
 ÒäËÒ² ÓÈ
[,]
αβ
¹¯ºÒÏ
mºÓãºº ¹º¯«}È Ò ºmãËmº¯«Ò² °ãºmÒ«ä
fk
k
()
() ; ,,,...
α
==
0012
 º¹Ë¯Èº¯ ÒÁÁ˯ËÓÒ¯ºmÈÓÒ«
Af
df
d
=
τ
Ò
()
Bf f d
=
∫
σσ
α
τ
 º¹Ë¯Èº¯ ÒÓ˯үºmÈÓÒ« ° ¹Ë¯ËäËÓÓ©ä m˯²ÓÒä
¹¯ËËãºä«mã«°«mÏÈÒäÓºº¯ÈÓ©äÒ
iË®°mÒËãÓº

() ()
ABf
d
d
fd f Ef
===
∫
τ
σσ τ
α
τ
Ò

() () ()
BAf
df
d
df faf Ef
==−==
∫
σ
στ τ
α
τ

~ÈäËÈÓÒ«
° sËã«m°«}ººãÒÓˮӺºº¹Ë¯Èº¯È°Ë°mËº¯ÈÓ©®º¹Ë¯È
º¯sȹ¯Òä˯ÓãËmº®º¹Ë¯Èº¯
O
ÓËÒäËËº¯ÈÓººiË®°mÒ
ËãÓº ¹°
oxO
=
ˆ
¹¯Ò m°Ë²
Λ∈∀
x
 ºÈ ã« ãºº
B
ÒäËË
äË°º
Λ∈∀== xoxOBxOB
,)
ˆ
(
ˆ
)
ˆ
ˆ
(
 Ò °ã˺mÈËãÓº ¯ÈmËÓ°mº

BO E
=
ÓËm©¹ºãÓ«Ë°«ÓÒ¹¯Ò}È}ºä
B

° |¯ÈÓ©® º¹Ë¯Èº¯ Ë°ãÒ °Ë°mË º ËÒÓ°mËÓËÓ º}ÈÎÒË
ªº °È亰º«ËãÓº Ò°¹ºãϺmÈm }È} ÈÓÈ㺠º}ÈÏÈËã°mº ãËää©

° { °ãÈË Ë°}ºÓËÓºä˯Ӻº ãÒÓˮӺº ¹¯º°¯ÈÓ°mÈ ÒÏ °ãºmÒ«

AB E=
äºÎË ÓË °ã˺mÈ m©¹ºãÓËÓÒË °ãºmÒ«

BA E=
 º
ÒäËË Óȹ¯Òä˯ äË°º m ¹¯º°¯ÈÓ°mË äÓººãËÓºm
P
nk
k
k
n
()
τατ
=
=
∑
0
ã«¹È¯©º¹Ë¯Èº¯ºm
A
Ò
B
Ë
B
Ë°º¹Ë¯Èº¯
äÓºÎËÓÒ«äÓººãËÓÈÓÈÓËÏÈmÒ°Òä¹Ë¯ËäËÓÓÈº¹Ë¯Èº¯
A
äÓººãËÓ
ατ
k
k
k
n
=
∑
0
°ÈmÒm°ººmË°mÒËäÓººãËÓ
ατ
k
k
k
n
−
=
∑
1
1

cÈÏËã 
ÒÓˮөËÏÈmÒ°Ò亰ˆÒmãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmË



    |¹¯ËËãËÓÒË           |¹Ë¯Èˆº¯ B  ÓÈÏ©mÈˈ°« viéjzt€u º¹Ë¯Èˆº¯‚ A  Ò º­ºÏÓÈÈˈ°« A −1 
    
                                   = BA
                           Ë°ãÒ AB      = E 
             
             
             
    ¯Òä˯                { ãÒÓˮӺä ¹¯º°ˆ¯ÈÓ°ˆmË Á‚Ó}Ò® f (τ )  ÒäË Ò² ÓÈ [α , β ]  ¹¯ºÒÏ
                    mºӂ     ã ­ºº    ¹º¯«}È   Ò      ‚ºmãˈmº¯« Ò²          ‚°ãºmÒ«ä

                            f   (k )
                                       (α ) = 0 ; k = 0,1,2,...  º¹Ë¯Èˆº¯ ÒÁÁ˯ËÓÒ¯ºmÈÓÒ«                                          = df  Ò
                                                                                                                                        Af
                                                                                                                                            dτ
                                        τ
                            = f (σ )dσ   º¹Ë¯Èˆº¯ Òӈ˯үºmÈÓÒ« ° ¹Ë¯ËäËÓÓ©ä m˯²ÓÒä
                           Bf ∫
                                        α
                           ¹¯ËËãºä«mã« ˆ°«mÏÈÒäÓºº­¯ÈˆÓ©äÒ
                           
                           iË®°ˆm҈Ëã Óº
                                                                        τ
                                                           = d
                                                          ABf
                                                               dτ       ∫ f (σ )dσ = f (τ ) = Ef Ò
                                                                        α
                                                                  τ
                                                            = df dσ = f (τ ) − f (a ) = f (τ ) = Ef
                                                                                                    
                                                          BAf  ∫ dσ
                                                               α
             
             
             
    ~ÈäËÈÓÒ«            ° sËã«m°«}ººãÒÓˮӺºº¹Ë¯Èˆº¯È°‚Ë°ˆm‚ˈº­¯ÈˆÓ©®º¹Ë¯È
                                       ˆº¯sȹ¯Òä˯ӂãËmº®º¹Ë¯Èˆº¯ O ÓËÒäËˈº­¯ÈˆÓººiË®°ˆmÒ
                                       ˆËã Óº ¹‚°ˆ  Oˆ x = o  ¹¯Ò m°Ë² ∀x ∈ Λ  ˆºÈ ã« ã ­ºº B  ÒäËˈ
                                       äË°ˆº ( Bˆ Oˆ ) x = Bˆ (Oˆ x ) = o ,
                                                                 ∀x ∈ Λ  Ò °ã˺mȈËã Óº ¯ÈmËÓ°ˆmº
                                       BO = E ÓËm©¹ºãӫˈ°«ÓÒ¹¯Ò}È}ºä B 
                                          
                           
                           ° |­¯ÈˆÓ©® º¹Ë¯Èˆº¯ Ë°ãÒ °‚Ë°ˆm‚ˈ ˆº ËÒÓ°ˆmËÓËÓ º}ÈÎ҈Ë
                                 ªˆº °È亰ˆº«ˆËã Óº Ò°¹ºã ϺmÈm }È} ÈÓÈ㺠º}ÈÏȈËã °ˆmº ãËää©
                                  
                           
                           ° { °ã‚ÈË ­Ë°}ºÓËÓºä˯Ӻº ãÒÓˮӺº ¹¯º°ˆ¯ÈÓ°ˆmÈ ÒÏ ‚°ãºmÒ«
                                         = E  äºÎˈ ÓË °ã˺mȈ  m©¹ºãÓËÓÒË ‚°ãºmÒ« BA
                                       AB                                                      = E  ˆº
                                       ÒäËˈ          Óȹ¯Òä˯           äË°ˆº          m       ¹¯º°ˆ¯ÈÓ°ˆmË                 äÓººãËÓºm
                                                    n
                                       Pn (τ ) =   ∑ α k τ k 㫹ȯ©º¹Ë¯Èˆº¯ºm A Ò B Ë B Ë°ˆ                               º¹Ë¯Èˆº¯
                                                   k =0

                                       ‚äÓºÎËÓÒ«äÓººãËÓÈÓÈÓËÏÈmÒ°Òä‚ ¹Ë¯ËäËÓӂ Ⱥ¹Ë¯Èˆº¯ A 
                                                           n                                                                        n
                                       äÓººãËӂ        ∑αk τ    k
                                                                       °ˆÈm҈m°ººˆmˈ°ˆmÒËäÓººãËÓ                          ∑ α k τ k −1 
                                                          k =0                                                                     k =1
             
             
             
             
             

Страницы