论文标题
阳性单变量痕量多项式
Positive univariate trace polynomials
论文作者
论文摘要
单变量痕量多项式是变量X和形式轨迹符号TR（X^J）中的多项式。可以在矩阵上自然评估这种表达，其中将痕量符号评估为归一化轨迹。本文解决了所有有限大小的对称矩阵上单变量多项式的全局阳性和约束阳性。给出了Artin对希尔伯特第17个问题的解决方案的奇特类似物：阳性的半决赛单变量痕量多项式是正方形产品和痕量多项式正方形痕迹的总和的商。
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses global and constrained positivity of univariate trace polynomials on symmetric matrices of all finite sizes. A tracial analog of Artin's solution to Hilbert's 17th problem is given: a positive semidefinite univariate trace polynomial is a quotient of sums of products of squares and traces of squares of trace polynomials.
