1. A personal authentication system comprising: a matrix generation unit configured to classify a plurality of feature amounts of face image data, which are recorded in advance, into classes and to calculate as a mapping matrix, coefficients of a linear discriminant equation which uses said recorded plurality of feature amounts as variables; a feature extraction unit configured to extract a first feature amount from first face image data and to extract a second feature amount from second face image data; a feature transformation unit configured to, by using said mapping matrix, transform said first feature amount into a first transformed feature amount and transform said second feature amount into a second transformed feature amount; a processing unit configured to calculate as a similarity, a normalized correlation value between said first transformed feature amount and said second transformed feature amount; and a data matching unit configured to judge that said first face image data and said second face image data are image data of same person when said similarity exceeds a predetermined threshold.