JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (4): 102-110.doi: 10.6040/j.issn.1671-9352.0.2020.492

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Properties for r-H-circulant matrices and polynomial algorithm of their inverse

LEI Lin, LI Xiao-li, HE Cheng-yuan*   

  1. School of Science, Xihua University, Chengdu 610039, Sichuan, China
  • Published:2021-04-13

Abstract: The concept of r-H-circulant matrices is proposed, and five equivalent conditions and two necessary and sufficient conditions for nonsingularity of r-H-circulant matrices are gained. Furthermore, utilizing the relationship between the r-H-circulant matrices and polynomial and the sufficient and necessary conditions for nonsingular and singular of r-H-circulant matrices, a polynomial algorithm for the inverse of the r-H-circulant matrices is given. Finally, a number of examples according to the structural characteristics of r-H-circulant matrices is provided.

Key words: r-H-circulant matrices, nonsingularity, inverse, reflexive generalized inverse, polynomial algorithm

CLC Number: 

  • O241.6
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