Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 290 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
°bkywvsvxztpmqwnéivsvql
¹¯Ò
sgn( ) sgn( ) sgn( ) sgn( )
λλλα
123 44
=− =− =−
′′

Ë°ãÒ
′′
=
α
44
0
°
Îtquprvtyx¹¯Ò
sgn( ) sgn( ) sgn( )
λλλ
123
==

°
Çvtyx¹¯Ò
sgn( ) sgn( ) sgn( )
λλ λ
12 3
==−

,,
˯m©®ÓËËÓ¯ÈãÓ©®°ãÈ®

λ
1
0≠

λ
2
0≠
Ò
λ
3
0=

º°ãË ¹Ë¯ËÓº°È ÓÈÈãÈ }ºº¯ÒÓÈ ¹¯Ò²ºÒä } ¯ÈmÓËÓÒ
02
44
3
342211
=
′′
+
′′′′
+
′′
+
′′
α
ξ
α
ξ
λ
ξ
λ
22
ã«}ºº¯ººm©Ëã«ËämȯÒÈÓ©
Ë°ãÒ
′′
≠
α
34
0
º¯ÈmÓËÓÒË¹¯ÒmºÒ°«}
02
3
342211
=
′′′′′′
+
′′′
+
′′′
ξ
α
ξ
λ
ξ
λ
22
ÒºÈÒäËËä
°
êssqwzq·nxrqpwjéjivsvql¹¯Ò
sgn( ) sgn( )
λλ
12
=

°
qwnéivsq·nxrqpwjéjivsvql ¹¯Ò
sgn( ) sgn( )
λλ
12
=−

Ë°ãÒ
′′
=
′′
≠
αα
34 44
00,
ºÒäËËä
°
Îtqupëssqwzq·nxrqp|qsqtlé¹ ¯ Ò
sgn( ) sgn( ) , ,
λα
i
i=
′′
=
44
12


°
 êssqwzq·nxrqp|qsqtlé ¹¯Ò
sgn( ) sgn( ) , ,
λα
i
i=−
′′
=
44
12


°
 qwnéivsq·nxrqp|qsqtlé¹¯Ò
sgn( ) sgn( )
λλ
12
=−

Ë°ãÒÎË
′′
=
′′
=
αα
34 44
00,
º

°
 Íjéjutqu}wnénxnrjíq}x¹wsvxrvxznp
¹¯Ò
sgn( ) sgn( )
λλ
i
=
2


°
 Íjéjwnénxnrjíq}x¹wsvxrvxznp
¹¯Ò
sgn( ) sgn( )
λλ
i
=−
2

,,,
{º¯º®ÓËËÓ¯ÈãÓ©®°ãÈ®

λ
1
0
≠
Ò
λλ
23
0
==

º°ãË¹Ë¯ËÓº°ÈÓÈÈãÈ}ºº¯ÒÓÈ¹¯Ò²ºÒä}¯ÈmÓËÓÒ
022
44
3
34
2
2411
=
′′
+
′′′′
+
′′′′
+
′′
α
ξ
α
ξ
α
ξ
λ
2

 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



              °bkywvsvxzt€pmqwnéivsvql
                                            ¹¯Ò sgn( λ1 ) = − sgn( λ2 ) = − sgn( λ3 ) = − sgn(α 44                       ′′ ) 
                 

        Ë°ãÒ α 44
                ′′ = 0 
                            
                 °Îtqu€prvtyx                                            ¹¯Ò sgn( λ1 ) = sgn( λ2 ) = sgn( λ3 ) 
                 
                 °Çvtyx                                                   ¹¯Ò sgn( λ1 ) = sgn( λ2 ) = − sgn( λ3 ) 
    
    
    
,, Ë¯m©®ÓËËӈ¯Èã Ó©®°ã‚È® λ 1 ≠ 0  λ 2 ≠ 0 Ò λ 3 = 0 


      º°ãË   ¹Ë¯ËÓº°È   ÓÈÈãÈ       }ºº¯ÒÓȈ           ¹¯Ò²ºÒä                                              }        ‚¯ÈmÓËÓÒ 
        λ1ξ1′′ + λ2ξ 2′′ + 2α 34
             2          2
                              ′′ ξ 3′′ + α 44
                                           ′′ = 0 ã«}ºˆº¯ººm©Ëã«ËämȯÒÈӈ©

        Ë°ãÒ α 34
                ′′ ≠ 0 ˆº‚¯ÈmÓËÓÒ˹¯Òmº҈°«} λ1ξ1′′′ 2 + λ2ξ 2′′′ 2 + 2α 34
                                                                                ′′′ ξ 3′′′ = 0 ÒˆºÈÒäËËä
               
               °êssqwzq·nxrqpwjéjivsvql                ¹¯Ò sgn( λ1 ) = sgn( λ2 ) 
               
               °­qwnéivsq·nxrqpwjéjivsvql               ¹¯Ò sgn( λ1 ) = − sgn( λ2 ) 
                 

        Ë°ãÒ α 34
                ′′ = 0 , α 44
                           ′′ ≠ 0 ˆºÒäËËä
    
                 °Îtqu€pëssqwzq·nxrqp|qsqtlé¹¯Ò sgn( λ i ) = sgn(α 44
                                                                           ′′ ) , i = 1,2 
                 
                 ° êssqwzq·nxrqp|qsqtlé         ¹¯Ò sgn( λ i ) = − sgn(α 44
                                                                                    ′′ ) , i = 1,2 
                 
                 ° ­qwnéivsq·nxrqp|qsqtlé       ¹¯Ò sgn( λ 1 ) = − sgn( λ 2 ) 
    
        Ë°ãÒÎË α 34
                   ′′ = 0 , α 44
                              ′′ = 0 ˆº
    
                 ° Íjéjutqu€}wnénxnrjíq}x¹wsvxrvxznp
                                               ¹¯Ò sgn( λ i ) = sgn( λ 2 ) 
                 
                 ° Íjéjwnénxnrjíq}x¹wsvxrvxznp      
                                               ¹¯Ò sgn( λ i ) = − sgn( λ 2 ) 
    
    
,,,{ˆº¯º®ÓËËӈ¯Èã Ó©®°ã‚È® λ1 ≠ 0 Ò λ 2 = λ 3 = 0 


      º°ã˹˯ËÓº°ÈÓÈÈãÈ}ºº¯ÒÓȈ¹¯Ò²ºÒä}‚¯ÈmÓËÓÒ 
      
                                                  λ1ξ1′′ 2 + 2α 24
                                                                ′′ ξ 2′′ + 2α 34
                                                                              ′′ ξ 3′′ + α 44
                                                                                           ′′ = 0 
        

Страницы