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F 11
F 21
= F 11
.
1
Λ 1 G 12
c 12
=
F 21 =
Λ 1 G 22 F 11
⇐⇒
(1.63)
Λ 1
c 12
G 12
c 22
c 22 −Λ 1
G 22
2nd left eigencolumn. Λ 2 :
c 11
F 21
F 22
= 0
,
Λ 2 G 11
Λ 2 G 12
c 12
(1.64)
Λ 2 G 12
Λ 2 G 22
c 12
c 22
0
1st identity:
( c 11 − Λ 2 G 11 ) F 21 +( c 12 − Λ 2 G 12 ) F 22 =0=
= F 22
.
F 12
F 22
c 12 −Λ 2
G 12
c 11 −Λ 2 G 11
1
c 12 Λ 2 G 12
c 11
= ⇒ F 12 =
Λ 2 G 11 F 22 ⇐⇒
(1.65)
Left conditions:
F 11
G 11
F 11
= 10
.
F 21
G 12
F 12
F l G l F l =I 2
⇐⇒
(1.66)
F 12
F 22
G 12
G 22
F 21
F 22
01
1st and 2nd partitioning:
[ F 11 ,F 21 ] G 11
F 11
F 21
=1 , [ F 12 ,F 22 ] G 11
F 12
F 22
=1 .
G 12
G 12
(1.67)
C 12
G 22
G 12
G 22
2nd identity:
=1
F 11 1 , −
C 11
1
c 12
Λ 1 G 12
c 22 − Λ 1 G 22
G 12
c 12 −Λ 1
G 12
G 12
G 22
Λ 1
c 22
G 22
=1
F 11 G 11
1
Λ 1 G 12
Λ 1 G 12
c 22 − Λ 1 G 22
G 12 c 12
G 22 c 12
⇐⇒
c 22 − Λ 1 G 22 ,G 12
c 12 Λ 1 G 12
c 22 −Λ 1
G 22
F 11 G 11
Λ 1 G 22 ) 2 =1
Λ 1 G 12
Λ 1 G 12 ) 2
2 G 12 c 12
Λ 1 G 22 + G 22 ( c 12
⇐⇒
c 22
( c 22
c 22 − Λ 1 G 22
= ⇒ F 11 = ±
( c 22
Λ 1 G 22 ) 2 G 11
Λ 1 G 12 )( c 22
Λ 1 G 22 ) G 12 +( c 12
Λ 1 G 12 ) 2 G 22
(1.68)
2( c 12
=
F 11
F 21
= F 11
1
⇐⇒
c 12 Λ 1 G 12
c 22 −Λ 1
G 22
1
( c 22
=
±
Λ 1 G 12 ) 2 G 22 ×
Λ 1 G 22 ) 2 G 11
Λ 1 G 12 )( c 22
Λ 1 G 22 ) G 12 +( c 12
2( c 12
c 22 − Λ 1 G 22
q. e. d.
×
( c 12
Λ 1 G 12 )
1st identity:
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