2024/07/23 by Frits Verhagen, Marco Tomamichel, Verhagen, Frits +3 · 3 citations
Computer Science · Mathematics · #Algorithm #Applied mathematics #Combinatorics #Computer science #Eigenvalues and eigenvectors #Face and Expression Recognition #Majorization #Materials science #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix algebra #Physics
paper · pdf · doi:10.1109/tit.2025.3585062
published in IEEE Transactions on Information Theory 71(9), 6517-6545 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2025/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We say that a matrixPwith non-negative entries majorizes another such matrixQif there is a stochastic matrixTsuch thatQ=TP. We study matrix majorization in large samples and in the catalytic regime in the case where the columns of the matrices need not have equal support, as has been assumed in earlier works. We focus on two cases: either there are no support restrictions (except for requiring a non-empty intersection for the supports) or the final column dominates the others. Using real-algebraic methods, we identify sufficient and almost necessary conditions for majorization in large samples or when using catalytic states under these support conditions. These conditions are given in terms of multivariate divergences that generalize the Rényi divergences. We notice that varying support conditions dramatically affect the relevant set of divergences. Our results find an application in the theory of catalytic state transformation in quantum thermodynamics.