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+//page 239

+//Example 7.3

+clc;

+clear;

+close;

+A = [5 -6 -6;-1 4 2;3 -6 -4];

+disp(A,'A = ');

+f = poly(A,"x");

+disp('Characteristic polynomial for linear operator T on R^3 will be:');

+disp(f,'f = ');

+disp('or');

+disp('(x-1)(x-2)^2');

+x = poly(0,"x");

+disp('The minimal polynomial for T is:');

+p = (x-1)*(x-2);

+disp(p,'p = ');

+disp('or');

+disp('p = (x-1)(x-2)');

+disp('So in cyclic decomposition of T, a1 will have p as its T-annihilator.');

+disp('Another vector a2 that generate cyclic subspace of dimension 1 will have its T-annihilator as p2.');

+p2 = x-2;

+disp(p2,'p2 = ');

+disp(p*p2,'pp2 = ');

+disp('i.e., pp2 = f');

+disp('Therefore, A is similar to B');

+B = [0 -2 0;1 3 0;0 0 2];

+disp(B,'B = ');

+disp('Thus, we can see thet Matrix of T in ordered basis is B');

+//end