Invertibility of circulant matrices of arbitrary size

Jeong Ok Choi, Youngmi Hur

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalLinear and Multilinear Algebra
DOIs
Publication statusAccepted/In press - 2021

Bibliographical note

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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