### 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.

raphaellae said...

professor that is so true about the truth. it is king of the holy oops wholly dark-we can't see it but we know what direction the living light is travelling in, sort of like chasing after a deceased pianist.

love and light and hugs.

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