论文标题
当地极限对正定矩阵的限制问题
Local extrema for Procustes problems in the set of positive definite matrices
论文作者
论文摘要
Given two positive definite matrices $A$ and $B$, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of $A$ and $B$ and those of $AB$ by means of majorization inequalities.在这项工作中，我们进行了一项本地研究，集中在实现这些不平等现象的矩阵的范围内。作为应用程序，我们完成了一些有关在正定矩阵的多种形式中对单位不变规范的问题的结果。
Given two positive definite matrices $A$ and $B$, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of $A$ and $B$ and those of $AB$ by means of majorization inequalities. In this work we make a local study focused in the spectrum of the matrices that achieve the equality in those inequalities. As an application, we complete some previous results concerning Procustes problems for unitarily invariant norms in the manifold of positive definite matrices.
