  In this work we analyze principle component analysis (PCA) as a deterministic
input-output system. We show that the relative information loss induced by
reducing the dimensionality of the data after performing the PCA is the same as
in dimensionality reduction without PCA. Finally, we analyze the case where the
PCA uses the sample covariance matrix to compute the rotation. If the rotation
matrix is not available at the output, we show that an infinite amount of
information is lost. The relative information loss is shown to decrease with
increasing sample size.
