2020/02/08 by Pablo Calderón, Calderón, Pablo, Noelia B. Rios +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2002.03052
openalex publication_date 2020/02/08 · openalex created_date 2020/02/14 · openalex updated_date 2026/07/28
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.