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+//page 294

+//Example 8.17

+//Equation given in example 14 is used.

+clc;

+clear;

+close;

+function [m] = transform(x,y,z)

+    x1 = 3*x;

+    x2 = 12*y;

+    x3 = -z;

+    m = [x1 x2 x3];

+endfunction

+

+disp('Matrix of projection E in orthonormal basis is:');

+t1 = transform(3,3,3);

+t2 = transform(12,12,12);

+t3 = transform(-1,-1,-1);

+A = [t1; t2; t3];

+disp(A,'A = 1/154  *  ');

+A1 = (conj(A))';

+disp(A1,'A* = ');

+disp('Since, E = E* and A = A*, then A is also the matrix of E*');

+a1 = [154 0 0];

+a2 = [145 -36 3];

+a3 = [-36 10 12];

+disp(a1,'a1 = ');

+disp(a2,'a2 = ');

+disp(a3,'a3 = ');

+disp('{a1,a2,a3} is the basis.');

+Ea1 = [9 36 -3];

+Ea2 = [0 0 0];

+Ea3 = [0 0 0];

+disp(Ea1,'Ea1 = ');

+disp(Ea2,'Ea2 = ');

+disp(Ea3,'Ea3 = ');

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

+disp('Matrix B of E in the basis is:');

+disp(B,'B = ');

+B1 = (conj(B))';

+disp(B1,'B* = ');

+disp('Since, B is not equal to B*, B is not the matrix of E*');

+//end