Skip to content
DraconiticResearch
Search Sources API
190,839 studies31 sourcesUpdated 37 min ago
PreprintCC BY-NC-ND 4.0arXiv

On e-doubly stochastic matrices over hyperbolic (polynomial) systems

  • Juyoung Jeong
  • M. Seetharama Gowda
  • Sudheer Shukla
Open at sourcePDFDOICite

Abstract

In the setting of a hyperbolic (polynomial) system (𝒱, p, e) of degree n, an n-tuple A = [ a1, a2, …, an ] is said to be an e-doubly stochastic 𝒱-matrix if each ai belongs to the hyperbolicity cone, has trace $1$, and a1 + a2 + … + an = e. In this article, we characterize linear preservers of such 𝒱-matrices, describe some connections between e-doubly stochasticity and majorization, and study extreme points of the set of all e-doubly stochastic 𝒱-matrices. We show, for example, that (i) when n>1, positive, unital, and trace-preserving transformations are (the only) linear transformations on 𝒱 that preserve e-doubly stochasticity; (ii) when A is e-doubly stochastic, the eigenvalue vector of the linear combination βˆ‘i=1n riai is majorized by the coefficient vector (r1, r2, …, rn)T ∈ ℝn; and (iii) when p is complete, e-doubly stochastic 𝒱-matrices induced by (generalized) Jordan frames are extreme points of the compact convex set of all e-doubly stochastic 𝒱-matrices.

Related

  1. Binary X-rays of doubly stochastic matrices
    Bangzheng Li, Yuewei Liu, Yuan Yao
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. A Note on the NP-Hardness on Quadratic Optimization over Doubly Stochastic Matrices and the Gromov-Wasserstein Problem
    Yong Sheng Soh
    arXivPreprintarXiv licenceFull textGeometry & topologyOptimisation & controlarXiv
  3. Facets of the X-ray polytope of doubly stochastic matrices
    Prashant Chaudhary, Kapil Khandelwal
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsGeometry & topologyarXiv
  4. All doubly stochastic solutions to AXA = XAX when A is a permutation matrix
    Bogdan D. DjordjeviΔ‡, NebojΕ‘a Č. DinčiΔ‡, Yingshan Chen
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsCombinatorics & discrete mathematicsarXiv
  5. Backward doubly stochastic differential equations with or without reflection under weak conditions
    Shuxian Gao, Ying Hu, Jiaqiang Wen
    HALPreprintCC BY-NC-ND 4.0Full textProbabilityHAL

Cite

BibTeXRIS
BibTeX
@misc{jeong2026edoubly,
  title = {{On $e$-doubly stochastic matrices over hyperbolic (polynomial) systems}},
  author = {Juyoung Jeong and M. Seetharama Gowda and Sudheer Shukla},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32349},
  eprint = {2609.32349},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32349},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On e-doubly stochastic matrices over hyperbolic (polynomial) systems
AU  - Juyoung Jeong
AU  - M. Seetharama Gowda
AU  - Sudheer Shukla
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32349
UR  - https://arxiv.org/abs/2609.32349
AB  - In the setting of a hyperbolic (polynomial) system (𝒱, p, e) of degree n, an n-tuple A = [ a_1, a_2, …, a_n ] is said to be an e-doubly stochastic 𝒱-matrix if each a_i belongs to the hyperbolicity cone, has trace $1$, and a_1 + a_2 + … + a_n = e. In this article, we characterize linear preservers of such 𝒱-matrices, describe some connections between e-doubly stochasticity and majorization, and study extreme points of the set of all e-doubly stochastic 𝒱-matrices. We show, for example, that (i) when n>1, positive, unital, and trace-preserving transformations are (the only) linear transformations on 𝒱 that preserve e-doubly stochasticity; (ii) when A is e-doubly stochastic, the eigenvalue vector of the linear combination βˆ‘_i=1^n r_ia_i is majorized by the coefficient vector (r_1, r_2, …, r_n)^T ∈ ℝ^n; and (iii) when p is complete, e-doubly stochastic 𝒱-matrices induced by (generalized) Jordan frames are extreme points of the compact convex set of all e-doubly stochastic 𝒱-matrices.
ER  -