Contractive real Hankel matrix completion and associated directed subgraphs

Authors

• Sangmin Chun, Chung-Ang University
• Jaewoong Kim, Korea Military Academy
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-9-2026

Abstract

We study the contractive real Hankel matrix completion problem and determine when a partially specified Hankel matrix admits a real contractive completion. Our approach refines Parrott's theorem within a block-matrix framework, allowing us to describe how the feasibility of completing a partial Hankel matrix depends on the contractive behavior of its smaller Hankel submatrices. We then relate these analytic conditions to the structure of the directed graph associated with the pattern of specified entries. In particular, for a well-posed Hankel pattern, we characterize the extension property (B) including the graph G(Pn) (n≥1) (see the definitions given below) in graph-theoretic terms by identifying the precise directed subgraphs that guarantee the existence of a contractive real Hankel completion. This yields a complete solution of the completion problem for a class of partial Hankel matrices considered and clarifies the interplay between block-matrix constructions, contractive extensions, and the combinatorial features of the underlying graph.

Comments

Original published version available at https://doi.org/10.1016/j.laa.2026.09.007.

Recommended Citation

Chun, Sangmin, Jaewoong Kim, and Jasang Yoon. “Contractive Real Hankel Matrix Completion and Associated Directed Subgraphs.” Linear Algebra and Its Applications, ahead of print, September 9, 2026. https://doi.org/10.1016/j.laa.2026.09.007.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Linear Algebra and its Applications

DOI

10.1016/j.laa.2026.09.007