On the eigenvectors of Toeplitz matrices
Х. Д. Икрамов · Moscow University Computational Mathematics and Cybernetics · 2015
Although every nonzero vector x ∈ C n can be an eigenvector of a nonscalar Toeplitz matrix T, this assertion is generally false if symmetry is additionally required of T. It is shown that every symmetric or skew-symmetric vector is an eigenvector of a symmetric Toeplitz (nonscalar) matrix. A problem in matrix analysis that results in the need to characterize such eigenvectors is described.