Faces can be represented efficiently as a weighted linear combination of the eigenvectors of a covariance matrix of face images. It has also been shown [ J. Opt. Soc. Am.4, 519– 524 ( 1987)] that identifiable faces can be made by using only a subset of the eigenvectors, i.e., those with the largest eigenvalues. This low-dimensional representation is optimal in that it minimizes the squared error between the representation of the face image and the original face image. The present study demonstrates that, whereas this low-dimensional representation is optimal for identifying the physical categories of face, like sex, it is not optimal for recognizing the faces (i.e., discriminating known from unknown faces). Various low-dimensional representations of the faces in the higher dimensions of the face space (i.e., the eigenvectors with smaller eigenvalues) provide better information for face recognition.