検算のため，ネット上にころがっている主成分分析の例題の行列を使ってみました．

共分散・分散行列を使うパターン

#!/usr/local/bin/octave -qf
M = [
8 9 4;
2 5 7;
8 5 6;
3 5 4;
7 4 9;
4 3 4;
3 6 8;
6 8 2;
5 4 5;
6 7 6;
]
mean_column_vec = mean(M)
r = 1 / rows( M )
Cov = r * ( M - kron( mean_column_vec, ones( rows(M), 1 ) ) )' * ( M - kron( mean_column_vec, ones( rows(M), 1 ) ) )
[ A, D ] = eig( Cov )

これを実行．

>octave correlation_coefficient_matrix.oct
M =
8   9   4
2   5   7
8   5   6
3   5   4
7   4   9
4   3   4
3   6   8
6   8   2
5   4   5
6   7   6
mean_column_vec =
5.2000   5.6000   5.5000
r =  0.10000
Cov =
4.16000   1.38000  -0.40000
1.38000   3.24000  -1.30000
-0.40000  -1.30000   4.05000
A =
-0.598619  -0.682981  -0.418560
-0.584278   0.014835   0.811418
0.547973  -0.730286   0.407931
D =
5.87310   0.00000   0.00000
0.00000   3.70232   0.00000
0.00000   0.00000   1.87458

相関係数行列を使うパターン

#!/usr/local/bin/octave -qf
M = [
8 9 4;
2 5 7;
8 5 6;
3 5 4;
7 4 9;
4 3 4;
3 6 8;
6 8 2;
5 4 5;
6 7 6;
]
C = corrcoef( M )
[ A, D ] = eig( C )

こいつを実行．

>octave variance_covariance_matrix.oct
M =
8   9   4
2   5   7
8   5   6
3   5   4
7   4   9
4   3   4
3   6   8
6   8   2
5   4   5
6   7   6
C =
1.000000   0.375889  -0.097451
0.375889   1.000000  -0.358875
-0.097451  -0.358875   1.000000
A =
0.4925880   0.6892523  -0.5313081
-0.7392991   0.0093340  -0.6733125
-0.4591230   0.7244613   0.5141615
D =
0.52668   0.00000   0.00000
0.00000   0.90266   0.00000
0.00000   0.00000   1.57066