## 1 feb. 2015

### Comparing PRCOMP and SVD for the eigenvalues calculation

PRCOMP calculates the Standard Deviation with the standard divisor (N-1), so in the output value “sdev”, we get the standard deviation of the column of the score matrix (n.a).

For example:
3.21983981   0.54314465     0.41112799      0.08351649
0.06957348     0.02994683

The square of this values are the variances
1.036737e+01   2.950061e-01    1.690262e-01    6.975004e-03
4.840470e-03  8.968124e-04

Using SVD, we get an output value “d”, with the square root of the eigenvalues. Using the same data:
39.9571612  6.7402479  5.1019641  1.0364124  0.8633842  0.3716303

The square of these value are the “eigenvalues”:
1596.5747310   45.4309414   26.0300382    1.0741506    0.7454323    0.1381091

In order to get the “eigenvalues” for the PRCOMP, we have to consider that they are divided by (N-1). In our case we have 155 samples, so (N-1) = 154.
1596.5747310   45.4309414   26.0300382    1.0741506    0.7454323    0.1381091

To see the % of explained variance we can use the value of each eigenvalue divided the sum of all of them
95.59      2.72      1.559    0.064     0.045

This information is provided  with the summary in PRCOMP:
summary(X1_prcomp)

Importance of components:
PC1        PC2       PC3       PC4       PC5
Standard deviation          3.2198    0.5431    0.41113   0.08352   0.06957
Proportion of Variance      0.9559    0.0272    0.01559   0.00064   0.00045
Cumulative Proportion       0.9559    0.9831    0.99873   0.99937   0.99982