clears all variables:
>>clear
closes all plots
>>close all
generates a 4X4 matrix of random values
>>A=rand(4);
generates a 20X4 matrix of zeros
x=zeros(4,20);
places non-zero values in the first column of x
>>x(:,1) = [0.4, 0.2, 0.1, 0.3]'
x =
  Columns 1 through 7
    0.4000         0         0         0         0         0         0
    0.2000         0         0         0         0         0         0
    0.1000         0         0         0         0         0         0
    0.3000         0         0         0         0         0         0
  Columns 8 through 14
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
         0         0         0         0         0         0         0
  Columns 15 through 20
         0         0         0         0         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0

iterates the map:
>> for ii = 1:19
>>      x(:,ii+1) = A*x(:,ii);
>> end


>>x(:,1:3)
ans =
    0.4000    0.3891    0.5919
    0.2000    0.4429    0.5838
    0.1000    0.3393    0.4970
    0.3000    0.1415    0.2517

>>x
x =
  Columns 1 through 7
    0.4000    0.3891    0.5919    0.8788    1.2933    1.9096    2.8177
    0.2000    0.4429    0.5838    0.8811    1.2966    1.9135    2.8238
    0.1000    0.3393    0.4970    0.7225    1.0709    1.5790    2.3302
    0.3000    0.1415    0.2517    0.3731    0.5471    0.8086    1.1929
  Columns 8 through 14
    4.1579    6.1356    9.0541   13.3607   19.7157   29.0935   42.9320
    4.1669    6.1490    9.0737   13.3897   19.7585   29.1567   43.0252
    3.4386    5.0742    7.4878   11.0493   16.3050   24.0605   35.5049
    1.7604    2.5978    3.8334    5.6568    8.3474   12.3179   18.1770
  Columns 15 through 21
   63.3527   93.4866  137.9537  203.5719  300.4015  443.2883  654.1398
   63.4903   93.6896  138.2534  204.0140  301.0540  444.2512  655.5606
   52.3930   77.3138  114.0884  168.3549  248.4334  366.6016  540.9767
   26.8229   39.5813   58.4083   86.1904  127.1872  187.6841  276.9567

matlab allows you to also multiply these matrices
to produce the final result.
>>xm = A^20*x(:,1);

>>xm
xm =
  654.1398
  655.5606
  540.9767
  276.9567

the results should the same for ii  = 21 
>>xm-x(:,21)
ans =
   1.0e-12 *
   -0.3411
   -0.2274
   -0.2274
         0
diary off