A note on the inverse eigenvalue problem for symmetric doubly stochastic matrices

摘要

In Hwang and Pyo [S.G. Hwang, S.S. Pyo, The inverse eigenvalue problem for symmetric doubly stochastic matrices, Linear Algebra Appl. 379 (2004) 77-83], it is claimed that : for a real n-tuple Lambda = (1, lambda(2), ..., lambda(n)) with 1 > lambda(2) >= ... >= lambda(n), if 1 + lambda 2(n - 1) + lambda 3/(n - 1)(n - 2) + ... + lambda n/2.1 >= 0, then there exists a symmetric positive doubly stochastic matrix whose spectrum is A. In this paper we give a counterexample to this proposition.