The inverse eigenvalue problem for real symmetric Toeplitz matrices

We show that every set of n real numbers is the set of eigenvalues of an n x n real symmetric Toeplitz matrix; the matrix has a certain additional regularity. The argument-based on the topological degree-is nonconstructive. AT&T BELL LABORATORIES, MURRAY HILL, NEW JERSEY 07974 E-mail address: hjlfresearch. att .com This content downloaded from 157.55.39.29 on Tue, 12 Apr 2016 08:53:54 UTC All use subject to http://about.jstor.org/terms