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Yundari, Yundari
Jurusan Matematika FMIPA Universtas Tanjungpura
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Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
Determinants of Tridiagonal and Circulant Matrices Special Form by Chebyshev Polynomials Nurliantika, Nurliantika; Fran, Fransiskus; Yundari, Yundari
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27871

Abstract

Along with the development of science, many researchers have found new methods to determine the determinant of a matrix of more than three orders. Chebyshev polynomial can be used to find and develop a more efficient formula in calculating the determinant of matrices. This research explores the Chebyshev polynomials of the first kind T_n (x) and second kind U_n (x). Both types of Chebyshev polynomials, T_n (x) and U_n (x), can be represented using recurrence relations. This research aims to determine the determinant of tridiagonal and circulant matrices of special form using Chebyshev polynomials T_n (x) and U_n (x). Determining the determinant of a matrix is a fundamental problem in linear algebra that plays an important role in both theoretical and applied mathematics. Its theoretical contributions include a deeper understanding of matrix properties, the development of efficient computational methods, and the explanation of the relationship between matrices and orthogonal polynomials. By utilizing Chebyshev polynomials, this study strengthens determinant theory, particularly for matrices with special shapes. The steps to determine the determinant of tridiagonal and circulant matrices involve the application of elementary row operations. The first step is to perform row operations on the tridiagonal and circulant matrices to obtain a matrix form that conforms to the determinant theorem of the tridiagonal and circulant matrices. After the elementary row operation is applied, if the form of the tridiagonal and circulant matrices each satisfies the form in the determinant theorem of the tridiagonal and circulant matrices, then the determinant of the matrices can be calculated using each of the theorems that satisfy. Then the determinants of the tridiagonal and the circulant matrices are obtained. The results of this study show that the determinant of tridiagonal and circulant matrices of special form can be determined using Chebyshev polynomials T_n (x) and U_n (x).
Co-Authors Adrian, Ferry Ahmad Yani T Alexander Ananda, Adelia Angraini, Wanda Aprizkiyandari, Siti Ariani, Prisilia Arizal, Arizal Asyrad, Adam Ayu Lestari Ayu Sri Utami Bambang Poniman Barita Riana Sitours Bayu Prihandono Brella Glysentia Vilgalita Chintya, Yuni Daniel Happy Putra Daska, Hipin Dea Rizki Darmawanti Dede Suratman Deni Winda Sari Desi Desi Ditanti Putri Shofia Eligia Helvianti Tri Lina P Elishabet Yohana Enis Rahayu Erlando Erlando Ervina Febyolga Evangelista, Gitta Evi Novian Evi Noviani Evy Sulistianingsih Fajria, Intan Luthfiani Fansiskus Fran Fikadila, Lisa Firhan Januardi Firmansyah, Dimas Fran, Fransiskus Fransiskus Fran Fransiskus Fran Hamdani Hamdani Hanssen, Calvin Helmi Helmi Helmi Helmi Helmi Helmi Helmi Hendra Perdana Hengki, Marius Henny Priandini Amalia Huda, Nur'ainul Miftahul HUDA, NUR’AINUL MIFTAHUL Huda, Nur’ainul Miftahul Ikbal Muhaimin Jonathan, Ryan Juwita, Dia Prima Laksono Trisnantoro Lauren, Nover Laurens Paskhia Dirda Rusanditia Lina Astuti Mariatul Kiftiah Martha, Shantika Meisita, Cheril Meliana Pasaribu Melinda Mareta Sari Mohamad Rif'at Mudinillah, Adam Muhammad Ilyas Mujiarti, Eka May Muslimah (F54210032) Nadia Putri Kurniawati Neno Juli Triami Neva Satyahadewi Nilamsari Kusumastuti Ningrum, Runi Aisyah Diyah Novia Kristefany Kabang Nurfadilah, Kori’ah NURFITRI IMRO’AH Nurfitri Im’roah Nurliantika, Nurliantika NUR’AINUL MIFTAHUL HUDA Pranata Anggi Puspita, Urfila Dian Putra, Fajar Rahmana Putri Romanda Rachmawati, Febby Rahmah, Mhaulia Ramadhan, Rahul Ramadhanti, Tasya Redika Rif'at, Mohammad Rifatullah, Rohit Riski Apriadi Rivaldi, Syahrul Rizki, Setyo Wira Ryan Jonathan Safitri, Fauziah Sasqia Aklysta Antaristi Setyo Wira Rizki Setyo Wira Rizki Shantika Martha Shantika Martha Silvia, Elma Silvy Heriyanti Suryani Suryani Takuan, Julianus Tambunan, Ayu Oktavia Tamtama, Ray Udjianna Sekteria Pasaribu Utriweni Mukhaiyar Venti, Monalisa Wele, Bruno Sala Winanda Epriyanti Yudhi Yulis Jamiah Zada Almira Zubaidah Zubaidah