DETERMINAN SUATU MATRIKS TOEPLITZ K-TRIDIAGONAL MENGGUNAKAN METODE REDUKSI BARIS DAN EKSPANSI KOFAKTOR

Rasmawati Rasmawati, Lailany Yahya, Agusyarif Rezka Nuha, Resmawan Resmawan

Abstract


This paper discusses the determinants of a k-tridiagonal Toeplitz matrix using row reduction and cofactor expansion methods. The analysis was carried out recursively from the general form of the determinant of the tridiagonal Toeplitz matrix, the determinant of the 2-tridiagonal Toeplitz matrix, and the determinant of the 3-tridiagonal Toeplitz matrix. In the end, the general form of the determinant of the k-tridiagonal Toeplitz matrix is obtained.

Keywords


Determinant; k-Tridiagonal Teoplitz Matrix; Row Reduction; Cofactor Expansion

Full Text:

PDF

References


H. Anton, Aljabar Linear Elementer, Jakarta: Erlangga, 1997.

D. K. Salkuyeh, “Positive Integer Powers of the Tridiagonal Toeplitz Matrices,” in International Mathematical Forum Ardabil, Iran, 2006.

B. Siregar, T. Tulus, and S. Sawaluddin, “Invers Suatu Matriks Toeplitz Menggunakan Metode Adjoin,” Saintia Matematika, vol. 2, No. 1, pp. 85-94, 2014.

J. Borowska, and L. Lacinska, “Eigenvalues of 2-Tridiagonal Toeplitz Matrix,” Jurnal of applied mathematics and computation mechanics, vol. 14, no. 4, pp. 11-17, 2015.

A. Z. Küçük, M. Özen, and H. Ince, H. “Recursive and combinational formulas for permanents of general k-tridiagonal Toeplitz matrices,” Filomat, vol. 33, no. 1, pp. 307-317, 2019.

C. M. da Fonseca, V. Kowalenko, and L. Losonczi, “Ninety years of k-tridiagonal matrices,” Studia Scientiarum Mathematicarum Hungarica, vol. 57, no. 3, 298-311, 2020.

A. Z. Kucuk, and M. Duz, “Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials,” Journal of Applied Mathematics and Computational Mechanics, vol. 16, no. 1, 2017.

A. Tănăsescu, and P.G. Popescu, “A fast singular value decomposition algorithm of general k-tridiagonal matrices,” Journal of Computational Science, vol. 31, pp. 1-5, 2019.

R. M. Gray, “Toeplitz and Circulant Matrices,” Departement of Electrical Engineering Stanford University., Stanford 94305, USA, 2005.

I. E. Wijayanti, S. Wahyuni, and Y. Susanti, Dasar-Dasar Aljabar Linear dan Penggunaannya dalam Berbagai Bidang, UGM PRESS, 2018.




DOI: https://doi.org/10.34312/euler.v9i1.10354

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Rasmawati Rasmawati, Lailany Yahya, Agusyarif Rezka Nuha, Resmawan Resmawan

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi has been indexed by:


                         EDITORIAL OFFICE OF EULER : JURNAL ILMIAH MATEMATIKA, SAINS, DAN TEKNOLOGI

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Tilongkabila, Kabupaten Bone Bolango 96119, Gorontalo, Indonesia
 Email: euler@ung.ac.id
 +62-852-55230451 (Call/SMS/WA)
 Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi (p-ISSN: 2087-9393 | e-ISSN:2776-3706) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.