Unusual Markov matrices

L^aT^eX

 \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.

Google glasses are better than wine

It occurred to me that RULE #$ applies to Google glasses. Why waste billions on a trophy husband or wife when you can just keep your Google glasses on all the time and there is no more need for re-constructive surgery or cosmetics. You can see whatever you want and live in a complete delusion. All the girls look better at closing time and opening time. You can just download a new look like ring tones. The advances in 3D visual field extraction allows complete VR immersion.
I can capture images and extract the 3 dimensional parallax data to a model and replaces surfaces with methods that are currently available. I could even imagine a cloud application for that. Don't give flowers, wine, chocolate  or diamonds on Valentine's day, give them a pair of Google glasses and become the object of their desire. ♥