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What it actually do is creating a representation of your input image. Read more into eigenfaces, which will explain the decomposition.

Basically, you have a set of eigenfaces, representing axes of a multidimensional space. There you want to transform your input image to and see which coördinates/parameters it gets for each axis. These results can than be compared with the parameters of stored faces by using a distance measure.

This link explains the principle a bit more: