论文标题
符号特征值和Lidskii型定理的衍生物
Derivatives of symplectic eigenvalues and a Lidskii type theorem
论文作者
论文摘要
与每$ 2N \ times 2n $ 2n $相关，真实的正定矩阵$ a，$存在$ n $的正数，称为$ a，$和$ \ mathbb {r}^{r}^{2n} $的符号eigenvalues称为符号的eigenbasis of $ a $ a $ a $ a $ a $ a $ a $。在本文中，我们讨论了符号特征值的可不同（分析性）和相应的符号特征性（分析）MAP $ t \ mapsto a（t），$和计算其衍生物。然后，我们得出了Lidskii定理的类似物，以作为一种应用程序。
Associated with every $2n\times 2n$ real positive definite matrix $A,$ there exist $n$ positive numbers called the symplectic eigenvalues of $A,$ and a basis of $\mathbb{R}^{2n}$ called the symplectic eigenbasis of $A$ corresponding to these numbers. In this paper, we discuss the differentiability (analyticity) of the symplectic eigenvalues and corresponding symplectic eigenbasis for differentiable (analytic) map $t\mapsto A(t),$ and compute their derivatives. We then derive an analogue of Lidskii's theorem for symplectic eigenvalues as an application.
