
86 ◾ System Instantaneous Availability
eorem 5.5: Matrix B has the characteristic root γ = 1, which is a simple root.
If X
0
= (x
1
, x
2
, …, x
2n+2
)
T
stands for the feature vector of γ = 1 on C, the value of
X
0
is unique and satisfies
+
xx
n
1
1
∏
()
=−λ
=
−
…
1
1,2,3,
0
2
1
x
D
ji n
i
j
i
∏
()
=−µ
++
=
−
…
1
1,2,3,
1
0
2
2
1
x
D
ji n
ni
j
i
.
In the formula,
∏
∑
∏
∑
() ()
=+ −λ
µ
=
−
=
+
=
−
=
+
Djj
j
i
i
n
j
i
i
n
21 1
0
2
2
1
0
2
2
1
.
Prove: According to eorem 5.4, γ = 1 is the simple characteristic root of
matrix B, which is equivalent to
−γ
γ
≠
γ=
dB I
d
0
1
. (5.6)
en, Formula 5.6 is proven:
−γ
γ
γ=
dB I
d
1
() () ()
()
()
() ()
()
()
()
=