LAUSR

Abstract The real (resp. symmetric) doubly stochastic inverse spectral problem is the problem of determining necessary and sufficient conditions for a real n-tuple λ = ( 1 , λ 2 , . . . , λ n ) to be the spectrum of an n × n (resp. symmetric) doubly stochastic matrix. If λ i ≤ 0 for all i = 2 , . . . , n and the sum of all the entries in λ is nonnegative, then we refer to such λ as a normalized Suleimanova spectrum. The purpose of this paper is to first fix an error in Theorem 9 of the recent paper Adeli et al. (2018) [1] , after giving a counterexample. Secondly, we give a negative answer to a question posed in Johnson and Paparella (2016) [3] concerning the realizability of normalized Suleimanova spectra for the case when n is odd. Some sufficient conditions for a positive answer to this question are given.