广义Schur-Horn定理与最优框架补
A generalized Schur-Horn theorem and optimal frame completions
摘要：
Schur-Horn定理是矩阵分析中的一个经典结果，它刻画了具有给定对角线和谱的正半定矩阵的存在性。近年来，这个定理被用来刻画有限框架的存在性，其元素具有给定的长度，其框架算子具有给定的谱。我们提供了一个新的推广的Schur-Horn定理，其特征在于所有可能的有限框架完成的频谱。也就是说，我们的框架运营商的频谱的有限框架，通过添加新的向量的长度给现有的框架。然后，我们利用这一特点，给出了一个新的和简单的算法计算最佳的完成。
英文摘要：
The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the existence of finite frames whose elements have given lengths and whose frame operator has a given spectrum. We provide a new generalization of the Schur-Horn theorem which characterizes the spectra of all possible finite frame completions. That is, we characterize the spectra of the frame operators of the finite frames obtained by adding new vectors of given lengths to an existing frame. We then exploit this characterization to give a new and simple algorithm for computing the optimal such completion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
