On the sum of left and right circulant matrices

被引：1

作者：

Lettington, Matthew C. ^{[1
]}

Schmidt, Karl Michael ^{[1
]}

机构：

[1] Cardiff Univ, Sch Math, 23 Senghennydd Rd, Cardiff CF24 4AG, Wales

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 658卷

关键词：

Circulant matrices; Discrete Fourier transforms; Moore-Penrose inverses; Sum-systems;

D O I：

10.1016/j.laa.2022.10.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider square matrices arising as the sum of left and right circulant matrices and derive asymptotics of the sequence of their powers. Particular emphasis is laid on the case where the matrix has consecutive integer entries; we find explicit formulae for the eigenvalues and eigenvectors of the matrix in this case and find its Moore-Penrose pseudoinverse. The calculation involves the discrete Fourier transform of integer vectors arising from sum systems and exhibits a resonance phenomenon. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页码：62 / 85

页数：24

共 11 条

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