### Unusual Markov matrices

LaTeX

\begin{bmatrix}
0.1 & 0.1\\
0.9 & 0.9\\
\end{bmatrix}

I was reviewing linear algebra again and decided to rummage around in Markov matrices to see what might be learned.

#include <stdio.h>
double x=11.0;
double y=23.40;

int main ( int argc, char* argv){
double xi=x;
double yi=y;
printf(" %f %f \n",x,y);
while((x-y)>0.000001 | (x-y)<-0.000001){
if (x==y){return 1;}
x=x+(yi*9.0)/10.0;
y=y+(xi*9.0)/10.0;
x=x-(xi*9.0)/10.0;
y=y-(yi*9.0)/10.0;
yi=y;xi=x;
printf(" %f %f \n",x,y);
}
}


This is just to see what happens when it is only slightly less than singular.
import numpy
from numpy import linalg
x=11.1
y=24.2
J=numpy.matrix([[0.1, 0.1001],[0.9,0.8999]])
K=numpy.matrix([[x],[y]])
print J**50
print linalg.solve(J,K)
print linalg.det(J)
print linalg.eig(J)

I find this particular matrix interesting because it oscillates and I am calling it "TWANG". The relationships can be adjusted to produce a damped oscillation at various rates, and it does function as an infinite series.

I think it might even have something to do with the rightful King of the wholly dark and vector of time's living light.