Numerical range of real-valued linear mapping on the complex Stiefel manifold: Convexity and application

Hanzhi Chen; Zhenhong Huang; Mengmeng Song; Yong Xia

doi:10.1016/j.laa.2025.01.031

Numerical range of real-valued linear mapping on the complex Stiefel manifold: Convexity and application

Hanzhi Chen
, Zhenhong Huang
, Mengmeng Song
, Yong Xia^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

Abstract

The study confirms the convexity of the joint numerical range of any k real-valued linear functions on the n×p complex Stiefel manifold under the condition k≤2n−2p+1. Revealing the hidden convexity of fractional linear programming on the complex Stiefel manifold, a first-time study, serves as an impactful application.

Original language	English
Pages (from-to)	95-110
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	710
DOIs	https://doi.org/10.1016/j.laa.2025.01.031
State	Published - 1 Apr 2025

Keywords

Complex Stiefel manifold
Convexity
Fractional linear programming
Numerical range

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10.1016/j.laa.2025.01.031

Cite this

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abstract = "The study confirms the convexity of the joint numerical range of any k real-valued linear functions on the n×p complex Stiefel manifold under the condition k≤2n−2p+1. Revealing the hidden convexity of fractional linear programming on the complex Stiefel manifold, a first-time study, serves as an impactful application.",

keywords = "Complex Stiefel manifold, Convexity, Fractional linear programming, Numerical range",

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AU - Chen, Hanzhi

AU - Huang, Zhenhong

AU - Song, Mengmeng

AU - Xia, Yong

PY - 2025/4/1

Y1 - 2025/4/1

N2 - The study confirms the convexity of the joint numerical range of any k real-valued linear functions on the n×p complex Stiefel manifold under the condition k≤2n−2p+1. Revealing the hidden convexity of fractional linear programming on the complex Stiefel manifold, a first-time study, serves as an impactful application.

AB - The study confirms the convexity of the joint numerical range of any k real-valued linear functions on the n×p complex Stiefel manifold under the condition k≤2n−2p+1. Revealing the hidden convexity of fractional linear programming on the complex Stiefel manifold, a first-time study, serves as an impactful application.

KW - Complex Stiefel manifold

KW - Convexity

KW - Fractional linear programming

KW - Numerical range

UR - https://www.scopus.com/pages/publications/85216474151

U2 - 10.1016/j.laa.2025.01.031

DO - 10.1016/j.laa.2025.01.031

M3 - 文章

AN - SCOPUS:85216474151

SN - 0024-3795

VL - 710

SP - 95

EP - 110

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Numerical range of real-valued linear mapping on the complex Stiefel manifold: Convexity and application

Abstract

Keywords

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