Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPLETION OF HANKEL PARTIAL CONTRACTIONS OF NON-EXTREMAL TYPE

  • KIM, IN HYOUN (Department of Mathematics Incheon National University) ;
  • YOO, SEONGUK (Department of Mathematics Inha University) ;
  • YOON, JASANG (School of Mathematical and Statistical Sciences The University of Texas Rio Grande Valley)
  • Received : 2014.11.27
  • Published : 2015.09.01
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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.

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References

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