有限Hurwitz矩阵的全非负性与多项式的根位置
Total nonnegativity of finite Hurwitz matrices and root location of polynomials
AI总结：
本文详细解释了拟稳定多项式的有限Hurwitz矩阵全非负性现象，并给出了实多项式具有全非负有限Hurwitz矩阵的充要条件。
摘要：
1970年，B.A. Asner Jr. 证明了对拟稳定多项式（即零点位于复平面闭左半平面的多项式），其有限Hurwitz矩阵是全非负的，即所有子式均为非负，且逆命题不成立。本文详细解释了这一现象，并给出了实多项式具有全非负有限Hurwitz矩阵的充要条件。
英文摘要：
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{closed} left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
