r-H-循环矩阵的性质及其逆的多项式算法

doi:10.6040/j.issn.1671-9352.0.2020.492

摘要/Abstract

摘要： 提出了r-H-循环矩阵的概念,并得到r-H-循环矩阵的五个等价条件和两个非奇异性的充要条件。此外,利用r-H循环矩阵与多项式之间的关系以及r-H循环矩阵非奇异性和奇异性的充要条件,给出r-H-循环矩阵逆的多项式算法。最后,根据r-H-循环矩阵的结构特点,给出了一些数值例子。

关键词: r-H-循环矩阵, 非奇异性, 逆, 自反广义逆, 多项式算法

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

中图分类号:

O241.6

雷林,李笑丽,何承源. r-H-循环矩阵的性质及其逆的多项式算法[J]. 《山东大学学报(理学版)》, 2021, 56(4): 102-110.

LEI Lin, LI Xiao-li, HE Cheng-yuan. Properties for r-H-circulant matrices and polynomial algorithm of their inverse[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(4): 102-110.

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