Direct Batch Evaluation of Desirable Eigenvectors of the DFT Matrix by Constrained Optimization

The process of the batch generation of orthonormal eigenvectors of a unitary matrix - like the DFT matrix - that are as close as possible to approximate eigenvectors having a desired feature - such as being samples of the Hermite Gaussian functions - is formulated as a constrained optimization problem. The adopted rationale is the collective evaluation of a complete set of eigenvectors in each eigenspace by the minimization of the squared Frobenius norm of the difference between the matrix whose columns are the sought vectors and the matrix whose columns are the corresponding approximate eigenvectors subject to the constraints that the sought vectors are orthonormal eigenvectors.