 a=[.5 .4 .1; .3 .4 .3; .1 .2 .7];
 a

a =

    0.5000    0.4000    0.1000
    0.3000    0.4000    0.3000
    0.1000    0.2000    0.7000

 sum(a)

ans =

    0.9000    1.0000    1.1000

 sum(a')

ans =

     1     1     1

 [v,d]=eig(a')

v =

    0.5000   -0.4657   -0.5000
   -0.8090   -0.5433   -0.3090
    0.3090   -0.6985    0.8090


d =

    0.0764         0         0
         0    1.0000         0
         0         0    0.5236

 pih=v(:,2)/sum(v(:,2))

pih =

    0.2727
    0.3182
    0.4091

 pih'*a

ans =

    0.2727    0.3182    0.4091

 a^2

ans =

    0.3800    0.3800    0.2400
    0.3000    0.3400    0.3600
    0.1800    0.2600    0.5600

 a^3

ans =

    0.3280    0.3520    0.3200
    0.2880    0.3280    0.3840
    0.2240    0.2880    0.4880

 a^10

ans =

    0.2733    0.3185    0.4081
    0.2729    0.3183    0.4088
    0.2722    0.3179    0.4099

 a^20

ans =

    0.2727    0.3182    0.4091
    0.2727    0.3182    0.4091
    0.2727    0.3182    0.4091

 pih

pih =

    0.2727
    0.3182
    0.4091

 exit

 1968 flop(s).

