2013/01/09 by Jun Zhu, Zhu, Jun, Changping Xiong +1
Computer Science · Mathematics · #15A04 #15A21 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Quantum Algebra (math.QA) #math.QA #msc:15A04 #msc:15A21
paper · pdf · doi:10.48550/arxiv.1301.1857
8 pages
openalex publication_date 2013/01/09 · arxiv created 2013/01/10 · arxiv updated 2013/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \Mn× n be the algebra of all n× n matrices. For x,y∈ Rn it is said that x is majorized by y if there is a double stochastic matrix A∈ Mn× n such that x=Ay (denoted by x\prec y). Suppose that Φ is a linear mapping from Rn into Rn, which is said to be strictly isotone if Φ(x)\prec Φ(y) whenever x\prec y. We say that an element α∈ Rn is a strictly all-isotone point if every strictly isotone φ at α (i.e. Φ(α)\precΦ(y) whenever x∈ Rn with α\prec x, and Φ(x)\precΦ(α) whenever x∈ Rn with x\prec α) is a strictly isotone. In this paper we show that every α=(α1,α2,...,αn)∈ Rn with α1>α2>...>αn is a strictly all-isotone point.