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

A periodic determinantal property for (0,1) double banded matrices

“…The main motivation to define this family was to prove two determinantal conjectures proposed in [12], for a = 1 and b = 0, or a = 0 and b = 1. In [11], it is proved that:…”

On determinantal recurrence relations of banded matrices

“…Both conjectures have recently attracted the attention of many researchers (Amanbek et al, 2020;Kurmanbek et al, 2020;Shitov, 2021).…”

Inverse properties of a class of seven-diagonal (near) Toeplitz matrices

“…In addition to the algorithmic development, many authors have contributed to the inverse properties of banded Toeplitz and near Toeplitz matrices, such as exact inverse formulas [10,5,22,17,23], bounds for entries of the inverse matrices, and bounds for the inverse norm. Examining formulas for determinant of such matrices can be also useful to explore the existence and uniqueness of solution related to the ordinary or partial differential problems [1,4,3,12,15].…”