Matriks Toeplitz dan Determinannya Menggunakan Metode Salihu

Miftahul Jannah -
Yusmet Rizal -

Abstract


The matrix is a rectangular array of numbers. In this range the numbers are called the entries of the matrix. In matrix calculations generally focus on square-shaped matrices. There is a matrix called the Toeplitz matrix. The Toeplitz matrix has the same operations and calculations as a square matrix in general, one method for calculating the determinant is the Sarrus method. There is an alternative method to solve the determinant of the matrix, namely the Salihu determinant. The purpose of this research is to know the determinant properties related to the Toeplitz matrix and to know the determinant of the n×n Toeplitz matrix with n≥3 using the Salihu method. The result of this study is that the completion of the Toeplitz matrix determinant calculation will produce the same value as the determinant calculation using the cofactor expansion method.

Full Text:

PDF

References


Arnellis. 2020. “The Effect of Realistic Mathematics Education Approach Oriented Higher Order Thinking Skills to Achievement Calculus”. Jurnal of Physics: Conference Series: 1-5.

Kariadinata, Rahayu. 2019. Aljabar Matriks Elementer. Bandung: CV Pustaka Setia.

Subiono. 2022. Aljabar: Suatu Pondasi Matematika. Surabaya: Institut Teknologi Sepuluh Nopember.

Gray, Robert M. 2005. Toeplitz and Circulan Matrices. Department of Electrical Engineering Stanford, USA.

Anton, Howard dan Rorres Chris. 2004. Aljabar Linear Elementer: Versi Aplikasi. Edisi 8. Jakarta:Erlangga

Wirawan, Nata. 2016. Matematika Ekonomi Lanjutan. Denpasar: Keraras Emas.

Aryani, Fitri, dkk. 2018. “Determinan Matriks Toeplitz Bentuk Khusus Menggunakan Ekspansi Kofaktor”. Jurnal Sains Matematika. Vol.04, No.2: 82-88

Bahota, Andi. 2014. ‘Menghitung Determinan Matriks n×n,(n≥3) dengan Menggunakan Metode Salihu’. JOM FMIPA. Vol.1. No.2: 344-350.

Salihu, A. 2012. ‘A New Method to Calculating Determinants of n×n (n≥3) Matrix, by Reducing Determinants to 2nd Order’. International Journal of Algebra. Vol.6, No. 19: 913-917.

Dwi, Sri Arttini. 2016. Matriks, Vektor & Terapannya di Bidang Teknik.Yogyakarta: Penerbit Andi.

Soebagyo, Joko. 2020. Matematika Teknik Aljabar Linier Matriks. Bandung: Manggu Makmur Tanjung Lestari.

Rainarli, Ednawati dan Dewi, Kania Evita. 2011. Aljabar Linear dan Matriks. Bandung: Universitas Komputer Indonesia.

Wedderburn. 1934. Lectures On Matrices. Providence, Rhode Island: American Mathematical Society.

Rasmawati, dkk. 2021. ‘Determinan Suatu Matriks Toeplitz k-Tridiagonal menggunakan metode reduksi baris dan ekspansi kofaktor’. Jurnal Ilmiah Matematika, Sains, dan teknologi. Vol.9, No.1:6-16.

Siregar, bakti, dkk. 2014. ‘Invers Suatu Matriks Toeplitz Menggunakan Metode Adjoin’. Jurnal Saintia Matematika. Vol.02, No.01:85-94.




DOI: http://dx.doi.org/10.24036/unpjomath.v8i2.14240