论文标题
$σ$ - 稳定矩阵
$σ$-Stable Matrices
论文作者
论文摘要
引入了$σ$ - 稳定的矩阵，并表明多项式的真实根包括特征多项式的系数表示系数符号变化。然后使用Obrechkoff的证明证明，当$ \ = $σ$ - 稳定矩阵的最大特征值位于$ \ mathbb {r} $中时，系数中最大的真实根是稳定性的最大根。然后讨论系数行为对缩放关系的某些含义。
$σ$-Stable matrices are introduced and it is shown that the real roots of the polynomials comprising the coefficients of the characteristic polynomial indicate the coefficient sign changes. A proof of Obrechkoff is then used to show that the largest real root from the coefficients is the point of stability when the maximal eigenvalue of the $σ$-stable matrix is in $\mathbb{R}$. Some implications of the coefficient behaviour for a scaling relation are then discussed.
