On Sat, Apr 19, 2003 at 03:03:44AM +0900, Chris Pine wrote:
> ----- Original Message -----
> From: "Chris Pine" <nemo / hellotree.com>
> 
> |  0,   0.5,  0.5  |
> |  .67, 0,    .33  |
> |  .67, .33,  0    |
> 
> 
> |  0,   .25,  .75  |
> |  1,   0,    0    |
> |  .33, .67,  0    |
> ----------------------------
> 
> Looking at this again, it seems that the latter matrix is flawed.  Not only
> is it uglier (a reasonable complaint), but it isn't "locally random", so to
> speak.  The long term probabilities are correct, but every 'b' is followed
> by an 'a'.

My bigger concern is that those columns don't add up to 1.
These aren't probability matrices.

> Perhaps a matrix is "naturally balanced" if the ratio of any two
> probabilities in any row is the same as the ratio of the corresponding
> probabilities in your initial vector (ignoring the zeros of the diagonal).

The idea I proposed was based on the objective of keeping the ratios the 
same (except for the event that is not supposed to repeat).

--
Daniel Carrera
Graduate Teaching Assistant.  Math Dept.
University of Maryland.  (301) 405-5137