Canonical Basis Vector and Some Other Issues

Please see the attached image. FYI: A1 = A2 means that smallest and largest eigenvalues of (V*)'(V) are equal, where V = [v1| v1*| v2| v2*| v3| v3*].

Do you guys think that the last sentence(~ centered tightly around 1) is correct? around "1" ?!?!

[Coding & Results]====================================================

clear all; clc;

mean1= 0;
std1 = 0.1;
x = randn(20);
x1 = x(:) - mean(x(:));
s = x1/std(x1)*std1;
out = reshape(s+ mean1, size(x));
[mean(out(:)),std(out(:))];

GauN(:,1) = out(:);
GauN_1 = GauN(:,1); Gaussian noise
la = 2.3129; eigenvalue 1 setting +-2.3129i (complex conjugate)
lb = 0.1765; eigenvalue 2 +-0.1765i
lc = 1.4861; eigenvalue 3 +-1.4861

Matrix = [0 la 0 0 0 0;...
-la 0 0 0 0 0;...
0 0 0 lb 0 0;...
0 0 -lb 0 0 0;...
0 0 0 0 0 lc;...
0 0 0 0 -lc 0];
[eigVc eigV] = eig(Matrix);

%--------------------------------------------------------------------------

M = 10;
V = eigVc (eigenvector set)
V_V = (V')*V;
eigenvalues = eig(V_V)
v1 = V(:,1);
v2 = V(:,3);
v3 = V(:,5);

%--------------------------------------------------------------------------

c1 = (1+GauN_1(10)).real(v1) + j.(1+GauN_1(20)).*imag(v1);
c2 = (1+GauN_1(30)).real(v2) + j.(1+GauN_1(40)).*imag(v2);
c3 = (1+GauN_1(50)).real(v3) + j.(1+GauN_1(60)).*imag(v3);
c = [c1+c2+c3];
h = sqrt((2*3)/M)*(c/norm(c));
hsquare = (norm(h))^2;

Origin_1 = ( ( v1'*h )^2 )/hsquare
Origin_2 = ( ( v2'*h )^2 )/hsquare
Origin_3 = ( ( v3'*h )^2 )/hsquare

Modi_1 = ( ( v1'*c )^2 )/norm(c(5:6,1))^2 (*partial norm)
Modi_2 = ( ( v2'*c )^2 )/norm(c(3:4,1))^2
Modi_3 = ( ( v3'*c )^2 )/norm(c(1:2,1))^2

%--------------------------------------------------------------------------
RESULTS:
V =
Columns 1 through 5
0.7071 + 0.0000i 0.7071 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.7071i 0.0000 - 0.7071i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.7071 + 0.0000i 0.7071 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.7071i 0.0000 - 0.7071i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.7071 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.7071i

Column 6
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.7071 + 0.0000i
0.0000 - 0.7071i

eigenvalues =
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000

Origin_1 = 0.3127
Origin_2 = 0.3482
Origin_3 = 0.3364

Modi_1 = 0.9284
Modi_2 = 0.9952
Modi_3 = 1.0738