We address a new general method for linear and nonlinear feature extraction for simultaneous representation and classification. We call this approach the maximum representation and discrimination feature (MRDF) method. We develop a novel nonlinear eigenfeature (NLEF) extraction technique to represent data with closed-form solutions and use it to derive a nonlinear MRDF algorithm. Results of the MRDF method on synthetic databases are shown and compared with results from standard Fukunaga-Koontz transform and Fisher discriminant function methods. The method is also applied to an automated product inspection problem (discrimination) and for classification and pose estimation of two similar objects under 3-D aspect angle variations (representation and discrimination).