Completion of Hankel partial contractions of non-extremal type

Authors

In Hyoun Kim
Seonguk Yoo
Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-1-2015

Abstract

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

Comments

©2015 Korean Mathematical Society.

The person using Journal of the Korean Mathematical Society Online may use, reproduce, disseminate, or display the open access version of content from this journal for non-commercial purposes.

Recommended Citation

Kim, In Hyoun, Seonguk Yoo, and Jasang Yoon. "Completion of Hankel partial contractions of non-extremal type." Journal of the Korean Mathematical Society 52, no. 5 (2015): 1003-1021. https://doi.org/10.4134/JKMS.2015.52.5.1003

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

Publication Title

Journal of the Korean Mathematical Society

DOI

10.4134/JKMS.2015.52.5.1003