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

Bakytzhan Kurmanbek, Yerlan Amanbek, Yogi A. Erlangga

2020

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DOI 10.1080/03081087.2020.1765959
Data confidence 70 medium
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Abstract

In this work, we present and prove the explicit formula for the determinant of a class of n×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.