[ATiNM] Eigen vectors

clc
clear all
close all

eps = 0.0005;

x = ones(3,1);
%A = [3 2 1; 2 8 4; 1 4 5];
 A = [1 2 3; 2 4 1; 3 1 6];

V = A * x;  % Move to upper scope

x_normalized = x;
max_val = 1e99;
max_val_old = 0;
diff = 1e99;

i = 0;
while true,
    diff = abs(abs(max_val) - abs(max_val_old));

    if abs(diff) < eps,
        break
    end

    %disp('**************');
    %fprintf('***   %d   ***\n', i);
    %disp('**************');

    old_v = V;
    V = A * x_normalized;

    max_val_old = max_val;
    max_val = max(V, [], 1)   ;

    x_normalized = V / max_val;
    i = i+1;
end

disp('*** Task 1 ***');
i
eigen_value = max_val
eigen_vector = V / max_val

disp('*** Task 2 ***');

V_1 = eigen_vector / sqrt(sum(eigen_vector, 1))
V1_V1T = V_1 * (V_1')

a_prim = A - eigen_value * V1_V1T