3 files changed, 88 insertions, 0 deletions
diff --git a/3293/CH7/EX7.3/Ex7_3.sce b/3293/CH7/EX7.3/Ex7_3.sce
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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
diff --git a/3293/CH7/EX7.6/Ex7_6.sce b/3293/CH7/EX7.6/Ex7_6.sce
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+//page 247
+//Example 7.6
+clc;
+clear;
+close;
+disp('A = ');
+disp('2   0   0');
+disp('a   2   0');
+disp('b   c   -1');
+a = 1;
+b = 0;
+c = 0;
+A = [2 0 0;a 2 0;b c -1];
+disp(A,'A = ');
+disp('Characteristic polynomial for A is:');
+disp(poly(A,"x"),'p = ');
+disp('In this case, minimal polynomial is same as characteristic polynomial.');
+disp('-----------------------------------------');
+a = 0;
+b = 0;
+c = 0;
+A = [2 0 0;a 2 0;b c -1];
+disp(A,'A = ');
+disp('Characteristic polynomial for A is:');
+disp(poly(A,"x"),'p = ');
+disp('In this case, minimal polynomial is:');
+disp('(x-2)(x+1)');
+disp('or');
+x = poly(0,"x");
+s = (x-2)*(x+1);
+disp(s);
+disp('(A-2I)(A+I) = ');
+disp('0    0   0');
+disp('3a   0   0');
+disp('ac   0   0');
+disp('if a = 0, A is similar to diagonal matrix.')
+//end
diff --git a/3293/CH7/EX7.7/Ex7_7.sce b/3293/CH7/EX7.7/Ex7_7.sce
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+//page 247
+//Example 7.7
+clc;
+clear;
+close;
+disp('A = ');
+disp('2   0   0   0');
+disp('1   2   0   0');
+disp('0   0   2   0');
+disp('0   0   a   2');
+disp('Considering a = 1');
+A = [2 0 0 0;1 2 0 0;0 0 2 0;0 0 1 2];
+p = poly(A,"x");
+disp('Characteristic polynomial for A is:');
+disp(p,'p = ');
+disp('or');
+disp('(x-2)^4');
+disp('Minimal polynomial for A =');
+disp('(x-2)^2');
+disp('For a = 0 and a = 1, characteristic and minimal polynomial are same.');
+disp('But for a=0, the solution space of (A - 2I) has 3 dimension whereas for a = 1, it has 2 dimension. ')
+//end