  Astronomy has evolved almost exclusively by the use of spectroscopic and
imaging techniques, operated separately. With the development of modern
technologies it is possible to obtain datacubes in which one combines both
techniques simultaneously, producing images with spectral resolution. To
extract information from them can be quite complex, and hence the development
of new methods of data analysis is desirable. We present a method of analysis
of datacube (data from single field observations, containing two spatial and
one spectral dimension) that uses PCA (Principal Component Analysis) to express
the data in the form of reduced dimensionality, facilitating efficient
information extraction from very large data sets. PCA transforms the system of
correlated coordinates into a system of uncorrelated coordinates ordered by
principal components of decreasing variance. The new coordinates are referred
to as eigenvectors, and the projections of the data onto these coordinates
produce images we will call tomograms. The association of the tomograms
(images) to eigenvectors (spectra) is important for the interpretation of both.
The eigenvectors are mutually orthogonal and this information is fundamental
for their handling and interpretation. When the datacube shows objects that
present uncorrelated physical phenomena, the eigenvector's orthogonality may be
instrumental in separating and identifying them. By handling eigenvectors and
tomograms one can enhance features, extract noise, compress data, extract
spectra, etc. We applied the method, for illustration purpose only, to the
central region of the LINER galaxy NGC 4736, and demonstrate that it has a type
1 active nucleus, not known before. Furthermore we show that it is displaced
from the centre of its stellar bulge.
