# Math Help - How to get Transition matrix from input/output distributions???

1. ## How to get Transition matrix from input/output distributions???

Hi,

Can you solve this?

[0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

[0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

[0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc

My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

Any thoughts appreciated.

2. Originally Posted by Trying
Hi,

Can you solve this?

[0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

[0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

[0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc

My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

Any thoughts appreciated.
$\vec a \cdot B = \vec c$

$\vec a^{-1} \cdot \vec a \cdot B = \vec a^{-1} \cdot \vec c$

$I \cdot B = \vec a^{-1} \cdot \vec c$

Just a thought...

3. Originally Posted by Trying
Hi,

Can you solve this?

[0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

[0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

[0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc

My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

Any thoughts appreciated.
You have:

$
\left[\begin{array}{ccc}
0.25 & 0.25 & 0.5\\
0.2083 & 0.4167 & 0.3750 \\
0.2327 & 0.4757 & 0.2917
\end{array}\right]\textbf{X}=
\left[\begin{array}{ccc}
0.2083 & 0.4167 & 0.3750\\
0.2327 & 0.4757 & 0.2917 \\
.. & .. & ..
\end{array}\right]
$

So to find $\textbf{X}$ you apply the inverse of the matrix multiplying it ..

CB