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.
|Number of pages||18|
|Journal||Linear and Multilinear Algebra|
|Publication status||Published - 2022|
Bibliographical noteFunding Information:
The first author is supported by the Institute for Basic Science [grant number IBS-R029-C1]. The second author acknowledges financial support from the National Research Foundation of Korea [grant numbers 2015R1A5A1009350], [grant number 2021R1A2C1007598].
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory