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

Bakytzhan Kurmanbek; Yerlan Amanbek; Yogi Erlangga

doi:10.1080/03081087.2020.1765959

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

Bakytzhan Kurmanbek, Yerlan Amanbek, Yogi Erlangga

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this work, we present and prove the explicit formula for the determinant of a class of (Formula presented.) 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.

Original language	English
Journal	Linear and Multilinear Algebra
DOIs	https://doi.org/10.1080/03081087.2020.1765959
Publication status	Accepted/In press - 2020

Keywords

Determinant
Toeplitz matrices

ASJC Scopus subject areas

Algebra and Number Theory

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title = "A proof of An{\d}eli{\'c}-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 (Formula presented.) nonsymmetric Toeplitz matrices. Setting up one of the nonzero subdiagonals to zero results in special pentadiagonal Toeplitz matrices, whose determinant formulas are conjectured by An{\d}eli{\'c} and Fonseca in An{\d}eli{\'c} [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",

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note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2020, {\textcopyright} 2020 Informa UK Limited, trading as Taylor & Francis Group. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

doi = "10.1080/03081087.2020.1765959",

language = "English",

journal = "Linear and Multilinear Algebra",

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AU - Kurmanbek, Bakytzhan

AU - Amanbek, Yerlan

AU - Erlangga, Yogi

N1 - Funding Information: 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. Publisher Copyright: © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - In this work, we present and prove the explicit formula for the determinant of a class of (Formula presented.) 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.

AB - In this work, we present and prove the explicit formula for the determinant of a class of (Formula presented.) 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.

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KW - Toeplitz matrices

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SN - 0308-1087

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

Abstract

Keywords

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