Doubly stochastic matrices with prescribed positive spectrum

Abstract We show that for every set Λ ={ λ 1 , λ 2 ,…, λ n } of real numbers such that λ 1 =1⩾λ 2 ⩾⋯⩾λ n >0 , there exists a doubly stochastic matrix with spectrum Λ. We present an explicit construction of such a matrix.