The main idea behind eigenfaces is that we want to learn a low-dimensional space - known as the eigenface subspace - on which we assume the faces intrinsically lie. From there, we can then compare faces within this low-dimensional space in order to perform facial recognition. It’s a relatively simple approach to facial recognition, but indeed one of the most famous and effective ones of the early approaches. It still works well in simple, controlled scenarios.
face recognition eigenfaces pca