-->A=[[0; .3],[1.6; .8]] // [Juveniles, Adults]'
 A  =
 
!   0.     1.6 !
!   0.3    0.8 !
 
-->x0=[15;10] // initial population
 x0  =
 
!   15. !
!   10. !
 
-->x=x0;for i=1:8, i, x=A*x, pop=sum(x,'r'), ratio=x(1,1)/x(2,1), end
 i  =
 
    1.  
 x  =
 
!   16.  !
!   12.5 !
 pop  =
 
    28.5  
 ratio  =
 
    1.28  
 i  =
 
    2.  
 x  =
 
!   20.  !
!   14.8 !
 pop  =
 
    34.8  
 ratio  =
 
    1.3513514  
 i  =
 
    3.  
 x  =
 
!   23.68 !
!   17.84 !
 pop  =
 
    41.52  
 ratio  =
 
    1.3273543  
 i  =
 
    4.  
 x  =
 
!   28.544 !
!   21.376 !
 pop  =
 
    49.92  
 ratio  =
 
    1.3353293  
 i  =
 
    5.  
 x  =
 
!   34.2016 !
!   25.664  !
 pop  =
 
    59.8656  
 ratio  =
 
    1.3326683  
 i  =
 
    6.  
 x  =
 
!   41.0624  !
!   30.79168 !
 pop  =
 
    71.85408  
 ratio  =
 
    1.333555  
 i  =
 
    7.  
 x  =
 
!   49.266688 !
!   36.952064 !
 pop  =
 
    86.218752  
 ratio  =
 
    1.3332594  
 i  =
 
    8.  
 x  =
 
!   59.123302 !
!   44.341658 !
 pop  =
 
    103.46496  
 ratio  =
 
    1.333358  
 
-->y=zeros(2,10)
 y  =
 
!   0.    0.    0.    0.    0.    0.    0.    0.    0.    0. !
!   0.    0.    0.    0.    0.    0.    0.    0.    0.    0. !
 
-->y(:,1)=x0
 y  =
 
!   15.    0.    0.    0.    0.    0.    0.    0.    0.    0. !
!   10.    0.    0.    0.    0.    0.    0.    0.    0.    0. !
 
-->for i=2:10, y(:,i)=A*y(:,i-1); end
 
-->y
 y  =
 
 
         column 1 to 8
 
!   15.    16.     20.     23.68    28.544    34.2016    41.0624     49.266688 !
!   10.    12.5    14.8    17.84    21.376    25.664     30.79168    36.952064 !
 
         column  9 to 10
 
!   59.123302    70.946652 !
!   44.341658    53.210317 !
 
-->plot(y(1,:),y(2,:),"d-");
 
-->// Change gears and watched an iterative approximation to largest eigenvalue
 
-->A=[2 0; 0 4]; x0 = x0/norm(x0)
 x0  =
 
!   0.8320503 !
!   0.5547002 !
 
-->y(:,1)=x0;
 
-->for i=2:10, y(:,i)=A*y(:,i-1); y(:,i) = y(:,i)/norm(y(:,i)); end
 
-->y
 y  =
 
 
         column 1 to 6
 
!   0.8320503    0.6    0.3511234    0.1842885    0.0933407    0.0468236 !
!   0.5547002    0.8    0.9363292    0.9828722    0.9956342    0.9989032 !
 
         column  7 to 10
 
!   0.0234311    0.0117179    0.0058593    0.0029297 !
!   0.9997255    0.9999313    0.9999828    0.9999957 !
 
-->// Note that we have rapidly found the second eigenvector [0, 1]^T
 
-->clf();plot(y(1,:),y(2,:),"d-");