论文标题
Lipschitz的稳定性$γ$ -Focs和RC规范Jordan基地，实际$ H $ - selfadchaint矩阵在小扰动下
Lipschitz stability of $γ$-FOCS and RC canonical Jordan bases of real $H$-selfadjoint matrices under small perturbations
论文作者
论文摘要
2008年，贝拉（Bella），奥尔什夫斯基（Olshevsky）和普拉萨德（Prasad）证明了h-selfadchoint矩阵的翻转正交（FO）基地是在小扰动下Lipschitz稳定的。在2022年，Dogruer，Minenkova和Olshevsky考虑了实际情况，并证明，对于真正的H-频道矩阵，存在一个更精致的基础，称为焦点基础。除了翻转的正交性外，它们还具有对称性（CS）特性。在本文中，我们证明了这些新的焦点在小扰动下也是Lipschitz稳定的。我们还建立了Lipschitz的稳定性，以实现经典的真实规范约旦基地。
In 2008 Bella, Olshevsky and Prasad proved that the flipped orthogonal (FO) Jordan bases of H-selfadjoint matrices are Lipschitz stable under small perturbations. In 2022, Dogruer, Minenkova and Olshevsky considered the real case, and proved that for real H-selfadjoint matrices there exist a more refined bases called FOCS bases. In addition to flipped orthogonality they also possess the conjugate symmetric (CS) property. In this paper we prove that these new FOCS bases are Lipschitz stable under small perturbations as well. We also establish the Lipschitz stability for the classical real canonical Jordan bases.
