  We study 16,707 quasar spectra from the SDSS using the Karhunen-Lo\`eve (KL)
transform (or Principal Component Analysis, PCA). The quasar eigenspectra of
the full catalog reveal the following: 1st order - the mean spectrum; 2nd order
- a host-galaxy component; 3rd order - the UV-optical continuum slope; 4th
order - the correlations of Balmer emission lines. We find that the spectral
classification of quasars is redshift and luminosity dependent, as such there
does not exist a compact set (< 10 modes) of eigenspectra (covering 900 to 8000
angstrom) which can describe most variations (> 95%) of the entire catalog. We
therefore construct several sets of eigenspectra in different redshift and
luminosity bins. From these eigenspectra we find that quasar spectra can be
classified (by the first two eigenspectra) into a sequence that is defined by a
simple progression in the steepness of the slope of the continuum. We also find
a dependence on redshift and luminosity in the eigencoefficients. The dominant
redshift effect is a result of the evolution of the blended FeII emission
(optical) and the Balmer continuum (the ``small bump''). A luminosity
dependence is also present in the eigencoefficients and is related to the
Baldwin effect. The eigenspectra constructed from the wavelength-selected SDSS
spectra are found to agree with the principal components by Francis et al.
(1992) and the well-known ``Eigenvector-1'' (Boroson and Green 1992).
(Abridged)
