Due to the growing interest in image classifiers, the concept of native two dimensional (2-D) classifiers continues to attract researchers in the field of pattern recognition. In most cases, the 2-D extension of a regular 1-D classifier is straightforward. Following the construction methodology of the Common Matrix Approach (CMA), its relation to the eigen-matrices of the covariance tensor is illustrated. The proposed methodology presents an alternative point of view to the classical CMA implementation that depends on Gram-Schmidt orthogonalization. Therefore a 2-D approach which is the counterpart of CVA implemented with covariance matrix is developed in this paper. (C) 2015 Elsevier Inc. All rights reserved.