Self-interlacing polynomials II: Matrices with selfinterlacing spectrum

Abstract

An n x n matrix is said to have a self-interlacing spectrum if its eigenvalues λk, k=1,…,n, are distributed as follows(equation found). A method for constructing sign definite matrices with self-interlacing spectrum from totally nonnegative ones is presented. This method is applied to bidiagonal and tridiagonal matrices. In particular, a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries is generalized.