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Invertibility of circulant matrices of arbitrary size

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Title
Invertibility of circulant matrices of arbitrary size
Author(s)
Jeong-Ok Choi; Hur, Youngmi
Publication Date
2022-12
Journal
Linear and Multilinear Algebra, v.70, no.21, pp.7057 - 7074
Publisher
Taylor and Francis Ltd.
Abstract
In this paper, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations of the entries in the first row with integer coefficients. Our result is general enough to show the invertibility of circulant matrices with any size and arrangement of entries. For example, using these conditions, we show the invertibility of the family of circulant matrices with particular forms of integers generated by a primitive element in (Formula presented.). Also, using a combinatorial structure of these sufficient conditions, we show invertibility for circulant 0, 1-matrices.
URI
https://pr.ibs.re.kr/handle/8788114/13278
DOI
10.1080/03081087.2021.1981812
ISSN
0308-1087
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > 1. Journal Papers (저널논문)
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