The revised direct batch evaluation algorithm of optimal eigenvectors of the DFT matrix using the notion of Moore-Penrose matrix pseudoinverse

The problem of batch generation of orthonormal Hermite-Gaussian-like eigenvectors separately for each eigenspace of the DFT matrix F is reconsidered. The singular value decomposition (SVD) technique is applied to a matrix whose columns are nonorthogonal eigenvectors lying in one eigenspace. Moreover this key matrix is allowed to be rank-deficient which necessitates the adoption of the notion of matrix pseudoinverse in order to find optimal orthonormal basis of that eigenspace. The contributed Revised Direct Batch Evaluation by constrained Optimization Algorithm using the notion of matrix Pseudoinverse (RDBEOAP) has been shown to give reasonable results for large values of the order N of matrix F - where the key matrix becomes rank deficient - compared to a similar technique (RDBEOA) based on the assumption that the key matrix has full rank.