论文标题
在对称谎言代数中的分析，可衡量和可测量的对角线化
Analytic, Differentiable and Measurable Diagonalizations in Symmetric Lie Algebras
论文作者
论文摘要
我们将线性算子的扰动理论概括为半神经正交对称谎言代数的设置。这些谎言代数为矩阵对角线化的各种概念提供了一个统一的框架，例如真实对称或复杂的Hermitian矩阵的特征值分解以及真实或复杂的奇异值分解。具体而言，在具有一定平滑度的结构化矩阵的路径上，我们研究了矩阵相应的对角线化可以获得的平滑度。
We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix diagonalization, such as the eigenvalue decomposition of real symmetric or complex Hermitian matrices, and the real or complex singular value decomposition. Concretely, given a path of structured matrices with a certain smoothness, we study what kind of smoothness one can obtain for the corresponding diagonalization of the matrices.
