论文标题
参数等级特征值的全局属性一个非结构化和结构化矩阵的扰动
Global properties of eigenvalues of parametric rank one perturbations for unstructured and structured matrices
论文作者
论文摘要
$ a+τuv^*$的特征值作为$τ\ in \ comp $或$τ\ in \ real $或$τ= \ e^{\ e^{\iiθ} $的函数。特别是，解决了特征值的全球分析公式存在问题。此外，详细讨论了具有$τ\至\ infty $的特征值的限制。考虑了以下矩阵类别：复杂（没有其他结构），真实（无其他结构），复杂的$ h $ - selfadjoint和真实的$ j $ -Hamiltonian。
General properties of eigenvalues of $A+τuv^*$ as functions of $τ\in\Comp$ or $τ\in\Real$ or $τ=\e^{\iiθ}$ on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with $τ\to\infty$ are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex $H$-selfadjoint and real $J$-Hamiltonian.
