Mathematical Theory of Networks and Systems pp 194-213
Spectral properties of finite Toeplitz matrices
- Cite this paper as:
- Delsarte P., Genin Y. (1984) Spectral properties of finite Toeplitz matrices. In: Fuhrmann P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg
The paper contains an investigation of certain spectral properties of finite Hermitian Toeplitz matrices. Some classical results relative to a constant Toeplitz matrix C are first extended to the polynomial matrix λI-C. Next, Carathéodory's representation based on the smallest eigenvalue of C is generalized to the case of an arbitrary eigenvalue. The splitting of each eigenspace of a real symmetric Toeplitz matrix C into its reciprocal and antireciprocal subspaces is then characterized. New identities are derived relating the characteristic determinants of the reciprocal and antireciprocal components of the Toeplitz submatrices of C. A special attention is brought to the inverse eigenvalue problem for Toeplitz matrices and some examples are given.
Unable to display preview. Download preview PDF.