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20240414IEEETG
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XingguoChen
20240414IEEETG
Commits
cdfb347a
Commit
cdfb347a
authored
May 17, 2024
by
LiXinwen
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merge conflict
parent
00666bc4
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2 changed files
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15 additions
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8 deletions
+15
-8
main/nonergodicity.tex
+2
-2
main/theorem.tex
+13
-6
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main/nonergodicity.tex
View file @
cdfb347a
...
...
@@ -66,8 +66,8 @@ b_{11} & b_{12} & \cdots & b_{1n} \\
c
_{
ij
}
=
\sum
_{
k=1
}^{
n
}
a
_{
ik
}
b
_{
kj
}
]
当
( i>j ) 时,有 ( c
_{
ij
}
=0 ),因为在此情况下,( a
_{
ik
}
=0 ) 或 ( b
_{
kj
}
=0 )
,乘积中至少有一项为 0。
所以
( C )
也是一个上三角矩阵。
当
$
i>j
$
时,有
$
c
_{
ij
}
=
0
$
,因为在此情况下,
$
a
_{
ik
}
=
0
$
或
$
b
_{
kj
}
=
0
$
,乘积中至少有一项为 0。
所以
$
C
$
也是一个上三角矩阵。
因此,证明了两个上三角矩阵的乘积还是一个上三角矩阵。
% N矩阵
...
...
main/theorem.tex
View file @
cdfb347a
...
...
@@ -82,18 +82,25 @@ P可以分解为Q R I 0,那么$N=(I-Q)^{-1}$,即描述了非吸收态之间
似乎论文可以从这方面下手!
% 2048游戏局面编码
\begin{equation}
$
p
=
2
^{
64
}
\cdot
\sum
_{
m
=
0
}^{
15
}
I
(
B
_
m
\neq
0
)
\cdot
2
^{
B
_
m
}
+
\sum
_{
m
=
0
}^{
15
}
(
1
\ll
4
m
)
\cdot
B
_
m
$
\end{equation}
% 马尔可夫链标准形式
[
P =
\begin{bmatrix}
Q
&
R
\
0
&
I
\begin{equation}
P =
\begin{bmatrix}
Q
&
R
\
\
0
&
I
\end{bmatrix}
]
\end{equation}
% 带策略的马尔可夫链标准形式
[ P
_
\pi
=
\begin{pmatrix}
Q
_
\pi
&
R
_
\pi
\
0
&
I
\end{pmatrix}
]
\begin{equation}
P
_
\pi
=
\begin{pmatrix}
Q
_
\pi
&
R
_
\pi
\\
0
&
I
\end{pmatrix}
\end{equation}
...
...
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