论文标题
在多项式上保存非负矩阵的猜想的证明
Proof of a conjecture on polynomials preserving nonnegative matrices
论文作者
论文摘要
我们考虑在R [X]中的多项式，这些多项式将给定顺序的非负（元素角度）矩阵映射到自身中。令n为正整数，并定义p（n）= {p in r [x]：p（a）是非负（元素，元素），对于所有a，a n-by-n非负（元素wise）矩阵}。该集合在非负逆特征值问题中起作用。克拉克（Clark）和爸爸（Paparella）猜想p（n+1）严格包含在p（n）中。我们证明了这个猜想。
We consider polynomials in R[x] which map the set of nonnegative (element-wise) matrices of a given order into itself. Let n be a positive integer and define P(n)= {p in R[x] : p(A) is nonnegative (element-wise), for all A, A an n-by-n nonnegative (element-wise) matrix}. This set plays a role in the Nonnegative Inverse Eigenvalue Problem. Clark and Paparella conjectured that P(n+1) is strictly contained in P(n). We prove this conjecture.
