Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 99 стр.

UptoLike

Составители: 

Рубрика: 

cÈÏËã

¯Ëº¯ÈϺmÈÓÒ«¹ãº°}º°Ò
cÈÏËã
cp|rck~|{ksjÐ|vz|vj
äÓºÎËÓÒËäÈ¯Ò
|¹¯ËËãËÓÒË

lÈ¯ÒÈ
C
¯ÈÏä˯È
m
[
n
°ªãËäËÓÈäÒ
γ
ji
injm,[,],[,]
∀= ∀=
11
ÓÈ
Ï©mÈË°« wévqoknlntqnu äÈ¯Ò©
A
¯ÈÏä˯È
m
[
l
° ªãËäËÓÈäÒ
α
jk
jmkl,[,], [,]
∀= =
11
 ÓÈ äÈ¯Ò
B
¯ÈÏä˯È
l
[
n
° ªãËäËÓÈäÒ
β
ki
klin,[,],[,]
∀= =
11
˰ãÒ
γ
αβ
ji jk ki
k
l
injm=∀==
=
1
11,[,],[,]

cËÏãÈ¹¯ºÒÏmËËÓÒ«äÈ¯ÒäȯÒÈ
C
˰äÈ¯ÒÈ¯ÈÏä˯È
m
[
n
¹¯Ò
síivu
l
 }ºº¯È« ººÏÓÈÈË°« }È}
CAB=
 ¯ÈmÒãº ÓȲºÎËÓÒ« }ºä¹ºÓËÓºm
¹¯ºÒÏmËËÓÒ« ¹º }ºä¹ºÓËÓÈä °ºäÓºÎÒËãË® äÈ¯ÒÓºº ¹¯ºÒÏmËËÓÒ« Òãã°¯Ò¯Ë
¯Ò°
¯Òä˯

¯ÒmËËä ¯ËÏãÈ© ¹¯ºÒÏmËËÓÒ« äÈ¯Ò ÒäËÒ² ÓË ºãËË Ëä
¹È¯°¯º}ÒãÒ°ºãºm
°°¯ÈÏä˯
A
˰
[
È¯ÈÏä˯
B

[
ºÈ¯ÈÏä˯
C
Ë
[

CAB== =
+
+
αα
αα
β
β
αβ αβ
αβ αβ
11 12
21 22
11
21
11 11 12 21
21 11 22 21

°
p°ãÒ¯ÈÏä˯
A
˰
[
È¯ÈÏä˯
B

[
º¯ÈÏä˯
C
Ë
[

CBA
== =
=+ +
ββ
αα
αα
αβ αβ αβ αβ
11 12
11 12
21 22
11 11 21 12 12 11 22 12
.
cÈÏËã
¯Ëº­¯ÈϺmÈÓÒ«¹ãº°}º°ˆÒ



             
             
             
             
             
             
             
cÈÏËã
cp|rck~|{ksjЁ|vz|v‘j
             
             
             
             
äÓºÎËÓÒËäȈ¯Ò
             
             
             
    |¹¯ËËãËÓÒË         lȈ¯ÒÈ C ¯ÈÏä˯È m[n °ªãËäËӈÈäÒ γ ji , ∀i = [1, n] , ∀j = [1, m] ÓÈ
    
                         Ï©mÈˈ°« wévqoknlntqnu äȈ¯Ò©                                     A  ¯ÈÏä˯È m[l ° ªãËäËӈÈäÒ
                          α jk , ∀j = [1, m] , ∀k = [1, l ]  ÓÈ äȈ¯Ò‚ B  ¯ÈÏä˯È l[n ° ªãËäËӈÈäÒ
                                                                                           l
                          βki , ∀k = [1, l ] , ∀i = [1, n] ˰ãÒ γ            ji   = ∑ α jk βki , ∀i = [1, n] , ∀j = [1, m] 
                                                                                          k =1
             
             cËς㠈Ȉ¹¯ºÒÏmËËÓÒ«äȈ¯ÒäȈ¯ÒÈ C ˰ˆ äȈ¯ÒȯÈÏä˯È m[n¹¯Ò
síivu l }ºˆº¯È« º­ºÏÓÈÈˈ°« }È} C = A B  ¯ÈmÒ㺠ÓȲºÎËÓÒ« }ºä¹ºÓËӈºm
¹¯ºÒÏmËËÓÒ« ¹º }ºä¹ºÓËӈÈä °ºäÓºÎ҈ËãË® äȈ¯ÒÓºº ¹¯ºÒÏmËËÓÒ« Òãã °ˆ¯Ò¯‚ˈ
¯Ò°
         
 ¯Òä˯        ¯ÒmËËä ¯Ëς㠈Ȉ© ¹¯ºÒÏmËËÓÒ« äȈ¯Ò ÒäË Ò² ÓË ­ºãËË Ëä
         ¹È¯‚°ˆ¯º}ÒãÒ°ˆºã­ºm
                
                                °‚°ˆ ¯ÈÏä˯ A ˰ˆ [ȯÈÏä˯ B [ˆºÈ¯ÈÏä˯
                                         C ­‚ˈ[
                                                                       α11 α12                 β11   α11 β11 + α12 β21
                                             C = A            B =                                  =                     
                                                                       α 21 α 22               β21   α 21 β11 + α 22 β21
                                                                                      

                                                                                      
    
                                °p°ãÒ¯ÈÏä˯ A ˰ˆ [ȯÈÏä˯ B [ˆº¯ÈÏä˯ C 
                                     ­‚ˈ[
                                                                                            α11 α12
                                             C = B            A = β11          β12                    =
                                                                                            α 21 α 22                             
                                                                   = α11 β11 + α 21 β12             α12 β11 + α 22 β12        .