On the spectra of close-to-Schwarz matrices Original Research Article

Several inverse eigenvalue problems for tridiagonal matrices are discussed. In particular, it is shown that for every set S of n complex numbers which is symmetric with respect to the real axis, there exists a symmetric in modulus tridiagonal n×n matrix A which has a nonnegative super diagonal, a nonpositive subdiagonal, all diagonal elements zero except for a11 which is nonnegative and ann which is nonpositive, and with spectrum S.