Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 254 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
° wãËäËÓ©
g
1

g
2

g
3
Ò
g
4
ãÒÓˮӺÓËÏÈmÒ°Òä©Ë¹º ¹ º°¯ºËÓÒÒº¯ÈÏÈ
ÏÒ° m
E
4
 jÓÈËºmº¯«}ÈΩ® ªãËäËÓÒÏ
E
4
äºÎË©¹¯Ë°ÈmãËÓÒ¹¯Ò
ºä ËÒÓ°mËÓÓ©ä º¯ÈϺä }È} ãÒÓË®ÓÈ« }ºäÒÓÈÒ« ªãËäËÓºm
g
1

g
2

g
3
Ò
g
4

|}È °ãËË º Ò°}ºä©® º¹Ë¯Èº¯
A
º¯ººÓÈãÓºº ¹¯ºË}Ò¯ºmÈÓÒ«
ªãËäËÓºm
E
4
ÓÈ
E
∗
ºãÎËÓºmãËmº¯«°ººÓºËÓÒ«ä
;
;
;
.
Ag g Ag g Ag o Ag o
11 2 2 3 4
====
{}ºº¯ÒÓÈÓºä¹¯Ë°ÈmãËÓÒÒªÒ¯ÈmËÓ°mÈäºÎÓº¹Ë¯Ë¹Ò°ÈmmÒË
0110
0101
1122
2111
ˆ
0010
0001
0022
0011
−
−
−−
=
−−
A

Òº}ºÓÈËãÓºmº°¹ºãϺmÈmÒ°¯ËÏãÈÈäÒ¹ÓÈ®Ëäº
6521
5621
2284
1142
0010
0001
0022
0011
0110
0101
1122
2111
ˆ
1
−−
−−
−
−−−−
=
−−
−
−
−−
=
−
A
~ÈäËÈÓÒË
˺äË¯ÒË°}È«ÒÓ˯¹¯ËÈÒ«º¯ººÓÈãÓºº¹¯ºË}Ò¯ºmÈÓÒ«m¹ºãÓËºË
mÒÓÈºÓÈ}ºªÈº¹Ë¯ÈÒ«Ò°¹ºãÏË°«Òm¯Ò²¹¯ÒãºÎËÓÒ«²
sȹ¯Òä˯ Ë°ãÒ
E
Ë° Ëm}ãÒºmº ¹¯º°¯ÈÓ°mº Ó˹¯Ë¯©mÓ©² ÓÈ
[,]
αβ
ÁÓ}Ò®°º°}È㫯өä¹¯ºÒÏmËËÓÒËä
∫
=
β
α
τττ
dyxyx )()(),(

È
E
∗
¹º¹¯º°¯ÈÓ°mº°˹ËÓÓ©²äÓººãËÓºm
P
nk
k
n
()
ττ
κ
=
=
∑
α
0
°˹ËÓÒÓË
m©Ë Ëä
n
 º º¯ººÓÈãÓÈ« ¹¯ºË}Ò«
x
()
τ
 ªãËäËÓÈ
E
ÓÈ
E
∗
äºÎË
¯È°°äÈ¯ÒmÈ°«}È}ÓÈÒãËËÓÈ
[,]
αβ
¹¯ÒãÒÎËÓÒË
x
()
τ
ãÒÓˮӺ®}ºä
ÒÓÈÒË® °˹ËÓÓ©²äÓººãËÓºmº¯ºÓº ªÈÏÈÈÈ¯È°°äº¯ËÓÈ m¹È¯È
¯ÈÁË
 Ë }  Ò Ò    } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



° wãËäËӈ© g1  g 2  g 3 Ò g 4 ãÒÓˮӺÓËÏÈmÒ°Òä©Ë¹º¹º°ˆ¯ºËÓÒ Òº­¯Èς ˆ­È
          ÏÒ°mE 4 jÓÈ˺mº¯«}ÈΩ®ªãËäËӈÒÏE 4 äºÎˈ­©ˆ ¹¯Ë°ˆÈmãËÓÒ¹¯Ò
          ˆºä ËÒÓ°ˆmËÓÓ©ä º­¯ÈϺä }È} ãÒÓË®ÓÈ« }ºä­ÒÓÈÒ« ªãËäËӈºm g1  g 2  g 3  Ò
           g 4 
          
          |ˆ}‚È °ãË‚ˈ ˆº Ò°}ºä©® º¹Ë¯Èˆº¯ A   º¯ˆººÓÈã Óºº ¹¯ºË}ˆÒ¯ºmÈÓÒ«
          ªãËäËӈºmE 4 ÓÈ E ∗ ºãÎËÓ‚ºmãˈmº¯«ˆ °ººˆÓº ËÓÒ«ä
          
                                           =g ;
                                          Ag                     =g ;
                                                                Ag                       = o;
                                                                                        Ag             =o .
                                                                                                      Ag
                                             1 1                   2 2                     3             4
          
          
          {}ºº¯ÒÓȈӺ乯˰ˆÈmãËÓÒÒªˆÒ¯ÈmËÓ°ˆmÈäºÎÓº¹Ë¯Ë¹Ò°Èˆ mmÒË
          
          
                                           −1       −1          0        0               −1     −1          1   2
                                               2        2       0        0                 2      2         1   1
                                                                           = Aˆ                                   
                                               1        0       0        0                 1      0        −1   0
                                               0        1       0        0                 0      1        −1   0
                                                
                                                
          Òº}ºÓȈËã Óºmº°¹ºã ϺmÈm Ò° ¯Ëς㠈ȈÈäÒ¹ÓÈ®Ë䈺
          
          
                                                                    −1
                                  −1     −1         1       2             −1      −1      0    0   −2           −4             −1   −1
                                   2       2        1       1                2      2     0    0   −4               8           2    2
                           Aˆ =                                                                  =                                       
                                   1       0       −1       0                1      0     0    0   −1               2           6   −5
                                   0       1       −1       0                0      1     0    0   −1               2        −5      6 
            
            
~ÈäËÈÓÒË˺äˈ¯ÒË°}È« Òӈ˯¹¯ËˆÈÒ«º¯ˆººÓÈã       Óºº¹¯ºË}ˆÒ¯ºmÈÓÒ«m¹ºãÓ˺Ë
                 mÒÓȺÓÈ}ºªˆÈº¹Ë¯ÈÒ«Ò°¹ºã ςˈ°«Òm¯‚Ò²¹¯ÒãºÎËÓÒ«²
                 
                 sȹ¯Òä˯ Ë°ãÒ E Ë°ˆ  Ëm}ãÒºmº ¹¯º°ˆ¯ÈÓ°ˆmº Ó˹¯Ë¯©mÓ©² ÓÈ [α , β ] 
                 Á‚Ó}Ò®°º°}È㫯ө乯ºÒÏmËËÓÒËä
                 
                                                                                   β
                                                                         ( x, y ) = ∫ x (τ ) y (τ )dτ 
                                                                                   α
                                                                                                                         n
                 È E ¹º¹¯º°ˆ¯ÈÓ°ˆmº°ˆË¹ËÓÓ©²äÓººãËÓºm Pn (τ ) =
                       ∗
                                                                                                                        ∑ α k τ κ °ˆË¹ËÓÒÓË
                                                                                                                        k =0
                 m© Ë Ëä n  ˆº º¯ˆººÓÈã ÓÈ« ¹¯ºË}Ò« x(τ )   ªãËäËӈÈ E ÓÈ E ∗  äºÎˈ
                 ¯È°°äȈ¯ÒmȈ °«}È}ÓÈÒã‚ ËËÓÈ [α , β ] ¹¯Ò­ãÒÎËÓÒË x(τ ) ãÒÓˮӺ®}ºä
                 ­ÒÓÈÒË®°ˆË¹ËÓÓ©²äÓººãËÓºmº¯º­ÓºªˆÈÏÈÈȯȰ°äºˆ¯ËÓÈm¹È¯È
                 ¯ÈÁË
                 

Страницы