Geography Reference
In-Depth Information
Table 22.29
Simultaneous diagonalization of the matrix pair (
G
l
,
G
r
): right
C
r
−
λ
i
G
l
F
1
r
=0
∀
i
∈{
1
,
2
}
(22.177)
subject to
G
r
=
I
3
(
tr
C
r
)
2
−
=
1
1
2
λ
1
,
2
=
λ
2
±
2
tr
C
r
±
4
det
C
r
(22.178)
1
Λ
1
,
2
1
λ
1
,
2
λ
1
,
2
Λ
1
,
2
=
=
(22.179)
“1st
right eigencolumn:
λ
1
”
F
1
r
:=
f
11
f
12
=
C
22
−
λ
1
1
(
c
22
−
(22.180)
−
C
12
λ
1
)
2
−
2
C
12
C
22
subject to
x
B
y
L
)
2
N
2
cos
2
Bx
B
y
B
+
M
2
x
L
y
L
C
12
=
−
(
x
L
y
B
−
(22.181)
x
B
y
L
)
2
N
2
cos
2
Bx
2
B
+
M
2
x
L
C
22
=(
x
L
y
B
−
(22.182)
“2nd
right eigencolumn:
λ
2
”
F
2
r
:=
f
21
f
22
=
−
C
12
+
λ
1
C
11
−
1
(
c
11
−
(22.183)
λ
2
λ
2
)
2
C
12
−
subject to
x
B
y
L
)
−
2
N
2
cos
2
By
B
+
M
2
y
L
C
11
=(
x
L
y
B
−
(22.184)
x
B
y
L
)
−
2
N
2
cos
2
Bx
B
y
B
+
M
2
x
L
y
L
C
12
=
−
(
x
L
y
B
−
(22.185)
“
Cartan 2-leg
”
∈
2
x
=
e
1
x
+
e
2
y
(22.186)
c
1
=
D
x
x
÷
D
x
x
=
e
1
(22.187)
c
2
=
D
y
x
÷D
y
x
=
e
2
(22.188)
“
right eigenvectors in the Cartan 2-leg
”
C
22
−
f
1
=
c
1
f
11
+
c
2
f
12
=
e
1
e
2
1
λ
1
(
c
22
−
(22.189)
−
C
12
λ
1
)
2
−
2
C
12
C
22
−
f
2
=
c
1
f
21
+
c
2
f
22
=
e
1
e
2
C
12
+
λ
2
C
22
−
1
(
c
11
−
(22.190)
λ
2
λ
2
)
2
C
12
−
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