Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvectors

An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition (EVD) with eigenvalues and eigenvectors. We have previously defined a discrete Fourier transform (DFT) domain algorithm which has been proven to extract the eigenvalues. The selection of as functions guarantees turn existence unique one-dimensional eigenspaces eigenvectors can exist. Determining such is not straightforward, requires three challenges be addressed. Firstly, subspaces for woven smoothly across DFT bins where non-trivial algebraic multiplicity causes ambiguity. Secondly, defined, phase smoothing aims minimum time support. Thirdly, we need check whether length, thus approximation order, sufficient. propose iterative extraction prove that this converges best set stationary points. provide number numerical examples simulation results, demonstrated ground truth arbitrarily closely.