2019/11/01 by M. Seetharama Gowda, Gowda, M. Seetharama
Computer Science · Engineering · #15A18 #15A48 #15B51 #15B57 #17C99 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1911.00579
openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an Euclidean Jordan algebra V of rank n, an element x is said to be\nmajorized by an element y, if the corresponding eigenvalue vector of x is\nmajorized by the eigenvalue vector of y in Rn. In this article, we describe\npointwise majorization inequalities of the form `T(x) majorized by S(x)', where\nT and S are linear transformations induced by Schur products. Specializing, we\nrecover analogs of majorization inequalities of Schur, Hadamard, and\nOppenheimer stated in the setting of Euclidean Jordan algebras, as well as\nmajorization inequalities connecting quadratic and Lyapunov transformations on\nV. We also show how Schur products induced by certain scalar means (such as\narithmetic, geometric, harmonic, and logarithmic means) naturally lead to\nmajorization inequalities.\n