A proof of Anđelić-Fonseca conjectures on the determinant of some Toeplitz matrices and their generalization

Abstract

In this work, we present and prove the explicit formula for the determinant of a class of $n\times n$ nonsymmetric Toeplitz matrices. Setting up one of the nonzero subdiagonals to zero results in special pentadiagonal Toeplitz matrices, whose determinant formulas are conjectured by Anđelić and Fonseca in Anđelić [Some determinantal considerations for pentadiagonal matrices. Linear Multilinear Algebra. 2020. DOI:10.1080/03081087.2019.1708845]. By using the explicit formula with this setting, the conjectures are therefore proved.

Keywords:

• Determinant
• Toeplitz matrices

Acknowledgments

BK would like to acknowledge the financial support by the FDCRG, Grant No 110119FD4502. YA wishes to acknowledge the research grant, No AP08052762, from the Ministry of Education and Science of the Republic of Kazakhstan and the Social Policy Grant of Nazarbayev University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

BK would like to acknowledge the financial support by the FDCRG, Grant No 110119FD4502. YA wishes to acknowledge the research grant, No AP08052762, from the Ministry of Education and Science of the Republic of Kazakhstan and the Social Policy Grant of Nazarbayev University.