Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 130 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
iË®°mÒËãÓº¹°
m
i
Ò
m
j
ÈË°¹º¯«º}ºË°
mm
ij
>
¹¯Ò
i<j
ºÈ
ÈË°¹º¯«º}ÒÒ°ãÈ
k
m
i
Ò
N
P
M
¹º°}ºã}ã«
∀=ik i
m
i
:
ÒÏÓÈÒ Ë
°¹¯ÈmËãÒmºÓ˯ÈmËÓ°mº
NLMN
PP
L
M
=<=
¹¯Ò
PP
LM
>

|}ºÓÈËãÓº¹ºãÈËä
det ( ) ... det
T
( , ,..., )
{, ,...,}
AA
kk k
kk nk
kk k
n
n
n
=− =
∑
1
12
12
12
12
ï
αα α

˺¯ËäÈº}ÈÏÈÓÈ

~ÈäËÈÓÒË

m˯ÎËÓÒË ˺¯Ëä©  º¹°}ÈË
°ãËÓÈã«ÓÒÓ˯¹¯ËÈÒ
{©ËãÒämäÈ¯ÒË
A
ªãËäËÓ©m²º
«ÒË m ÓË}ºº¯ºË °ãÈÈËäºË º¹¯ËËãË
ÓÒ«Ò°ºËÒÓÒäÒ²º¯ËÏ}ÈäÒ¹¯«
䩲}È}¹º}ÈÏÈÓºÓÈ¯Ò°
~ÈäËÒä º ¹È¯È ªãËäËÓºm
i
ik
α
Ò
j
jk
α
ÈË Ë°¹º¯«º} Ë°ãÒ °ºËÒÓ«Ò® Ò²
º¯ËϺ} ÒäËË Ù¹ºãºÎÒËãÓ©®µ ÓÈ}ãºÓ
ºË°¹¯Èm©®}ºÓËº¯ËÏ}È¯È°¹ºãºÎËÓ
m©ËãËmºº

ααα α
ααα α
ααα α
ααα α
11 12 13 1
21 22 23 2
31 32 33 3
123
...
...
...
... ... ... ... ...
...
n
n
n
nnn nn
èqxytvr
|ËmÒÓº º ¹¯Ò ¯ÈÓ°¹ºÓÒ¯ºmÈÓÒÒ }mȯÈÓº® äÈ¯Ò© Ò°ãº º
¯ËÏ}ºm°Ù¹ºãºÎÒËãÓ©äµÓÈ}ãºÓºäÓËäËÓ«Ë°«¹ºªºäÓËäËÓ«Ë°«
ÒÏÓÈ}}Èκ º°ãÈÈË人mÁº¯äãËÒ °ã˺mÈËãÓºÏÓÈËÓÒË
º¹¯ËËãÒËã«
vãË°mÒË

{°«}ºË °mº®°mº º¹¯ËËãÒËã« äÈ¯Ò© °Áº¯äãÒ¯ºmÈÓÓºË ã« ËË
°ºãºm¹¯ÒäËÓÒäº}ËË°¯º}ÈäÒÓȺº¯º
˺¯ËäÈ

¯Ò¹Ë¯Ë°ÈÓºm}Ë m²°ºãºmäÈ¯Ò©ÏÓÈ}ËËº¹¯ËËãÒËã«äË
Ó«Ë°«ÓÈ¹¯ºÒmº¹ºãºÎÓ©®
iº}ÈÏÈËã°mº
cÈ°°äº¯ÒämÓÈÈãË°ãÈ®}ºÈ¹Ë¯Ë°Èmã«°«xvxnltqn°ºã©º°}ºã}
ºÒ® mÒ°ãÈÈË䩲 m m©¯ÈÎËÓÒÒ ã« º¹¯ËËãÒËã« ÈË°« Áº¯ä㺮
n
nii
nkkk
kkkkk
ααα
...)1(
21
121
21
)...,,,...,,(
+
−
ºº°ÈºÓº¹º}ÈÏÈºÒ°ãºË°¹º¯«
}ºmÒÏäËÓÒ°«¹¯Ò¹Ë¯Ë°ÈÓºm}Ë°º°ËÓÒ²°ºãºmÓÈËÒÓÒ
 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



         iË®°ˆm҈Ëã Óº¹‚°ˆ  mi Ò m j È ˆ­Ë°¹º¯«º}ˆºË°ˆ  mi > m j ¹¯Ò i P M 
                                                          L                      M
          

                                                                             ∑ ( −1) ï ( k ,k ,...,k ) α1k α 2 k
                                                               T
          |}ºÓȈËã Óº¹ºã‚ÈËä det A                             =                        1   2   n
                                                                                                          1        2
                                                                                                                       ... α nkn = det A 
                                                                       {k1 ,k2 ,..., kn }
          
     ‘˺¯ËäȺ}ÈÏÈÓÈ
              
              
              
 ~ÈäËÈÓÒË              ˆm˯ÎËÓÒË ˆËº¯Ëä©  º¹‚°}Èˈ 
                  °ãË‚ ‚ ÓÈã«ӂ Òӈ˯¹¯ËˆÈÒ       
                         
                                                                                                        α11 α12 α13 ... α1n
                         {©ËãÒämäȈ¯ÒË A ªãËäËӈ©m²º
                                                                                    α21 α22 α23 ... α2n
                         «ÒË m ÓË}ºˆº¯ºË °ãÈÈËäºË º¹¯ËËãË
                         ÓÒ«Ò°ºËÒÓÒäÒ²ºˆ¯ËÏ}ÈäÒ¹¯«                   α31 α32 α33 ... α3n
                         䩲}È}¹º}ÈÏÈÓºÓȯҰ                                            
                         
                                                                                    ... ... ... ... ...
                         ~ÈäˈÒä ˆº ¹È¯È ªãËäËӈºm α ik i  Ò α jk j        αn1 αn2 αn3 ... αnn
                         Èˈ ­Ë°¹º¯«º} Ë°ãÒ °ºËÒÓ« Ò® Ò² 
                         ºˆ¯ËϺ} ÒäËˈ Ù¹ºãºÎ҈Ëã Ó©®µ ÓÈ}ãºÓ 
                         ˆºË°ˆ ¹¯Èm©®}ºÓ˺ˆ¯ËÏ}ȯȰ¹ºãºÎËÓ 
                         m© ËãËmºº                                        èqxytvr
              
                         |ËmÒÓº ˆº ¹¯Ò ˆ¯ÈÓ°¹ºÓÒ¯ºmÈÓÒÒ }mȯȈӺ® äȈ¯Ò© Ұ㺠ºˆ
                         ¯ËÏ}ºm°Ù¹ºãºÎ҈Ëã Ó©äµÓÈ}ãºÓºäÓËäËӫˈ°«¹ºªˆºä‚ÓËäËӫˈ°«
                         Ò ÏÓÈ} }Èκº °ãÈÈË人 m Áº¯ä‚ãË  Ò °ã˺mȈËã Óº ÏÓÈËÓÒË
                         º¹¯ËËã҈Ëã«
              
              
              
 vãË°ˆmÒË              {°«}ºË °mº®°ˆmº º¹¯ËËã҈Ëã« äȈ¯Ò© °Áº¯ä‚ãÒ¯ºmÈÓÓºË ã« ËË
                  °ˆºã­ºm¹¯ÒäËÓÒäº}ËË°ˆ¯º}ÈäÒÓȺ­º¯ºˆ
              
              
              
 ‘˺¯ËäÈ               ¯Ò¹Ë¯Ë°ˆÈÓºm}Ë m‚²°ˆºã­ºmäȈ¯Ò©ÏÓÈ}Ë˺¹¯ËËã҈Ëã«äË
                  ӫˈ°«Óȹ¯ºˆÒmº¹ºãºÎÓ©®
              
              
  iº}ÈÏȈËã°ˆmº
   
      cÈ°°äºˆ¯ÒämÓÈÈãË°ã‚È®}ºÈ¹Ë¯Ë°ˆÈmã« ˆ°«xvxnltqn°ˆºã­©º°}ºã }‚
      º­Ò® mÒ °ãÈÈË䩲 m m©¯ÈÎËÓÒÒ ã« º¹¯ËËã҈Ëã« Èˈ°« Áº¯ä‚㺮
           (−1) ( k1 , k 2 ,..., k i , k i +1 ..., k n ) α1k1α 2k 2 ...α nk n ˆºº°ˆÈˆºÓº¹º}ÈÏȈ ˆºÒ°ãº­Ë°¹º¯«
          }ºmÒÏäËÓ҈°«¹¯Ò¹Ë¯Ë°ˆÈÓºm}Ë°º°ËÓÒ²°ˆºã­ºmÓÈËÒÓÒ‚
          

Страницы