Parametric toeplitz systems

This paper investigates the properties of the two-variable polynomialu (, z) built on the first column of the adjoint matrix ofI -C, whereC is a given Hermitian Toeplitz matrix. In particular, the stability properties ofu (,z) are discussed and are shown to depend essentially on the location of X with respect to the eigenvalues ofC. The eigenvectors ofC, which have recently found some applications in signal processing and estimation theory, are obtained from the polynomialu(,z) when tends to the eigenvalues ofC. This allows one to derive several results concerning the eigenpolynomials, including those for the case of multiple eigenvalues.