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All Journal Jurnal Teknologi Industri Pertanian CAUCHY: Jurnal Matematika Murni dan Aplikasi TELKOMNIKA (Telecommunication Computing Electronics and Control) JREC (Journal of Electrical and Electronics) Jurnal Ilmu Komputer dan Agri-Informatika Jurnal Karya Pendidikan Matematika Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Krea-TIF: Jurnal Teknik Informatika Jambura Journal of Mathematics Jurnal Matematika UNAND Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif Jurnal Sistem Informasi MILANG Journal of Mathematics and Its Applications
Sugi Guritman
Department Of Mathematics, Faculty Of Science And Mathematics, IPB University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680,
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Library & Information Science Mathematics Mechanical Engineering Medicine & Pharmacology Physics Transportation

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A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE Guritman, Sugi; Jaharuddin; Mas'oed, Teduh Wulandari; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.69-80

Abstract

In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.
DETERMINAN, INVERS, DAN NILAI EIGEN MATRIKS SKEW-CIRCULANT DENGAN ENTRI BARISAN GEOMETRI Azhari, Mirza Farhan; Wulandari Mas'oed, Teduh; Guritman, Sugi; Jaharuddin; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 2 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.2.129-140

Abstract

Matriks skew-circulant adalah matriks segi yang entri terakhir setiap baris berpindah ke posisi utama dan berganti tanda disertai pergeseran semua entri lainnya ke posisi berikutnya. Dalam artikel ini, entri dari matriks circulant berupa entri barisan bilangan geometri. Tujuannya adalah merumuskan suatu formulasi sederhana dari determinan, invers, dan nilai eigen dari suatu matriks skew circulant. Formulasi determinan ditentukan dengan menerapkan serangkaian operasi baris dasar dan kolom dasar sampai diperoleh matriks diagonal. Langkah untuk mencari invers dilakukan dengan mengadaptasi metode dalam mencari determinan dan ekuivalensi baris dan kolom pada matriks. Dalam mencari nilai eigen digunakan konsep akar kesatuan (roots of unity) dan subgrup siklik.
On the Explicit Formula for Eigenvalues, Determinant, and Inverse of Circulant Matrices Aliatiningtyas, Nur; Guritman, Sugi; Wulandari, Teduh
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 3 (2022): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i3.8616

Abstract

Determining eigenvalues, determinants, and inverse for a general matrix is computationally hard work, especially when the size of the matrix is large enough. But, if the matrix has a special type of entry, then there is an opportunity to make it much easier by giving its explicit formulation. In this article, we derive explicit formulas for determining eigenvalues, determinants, and inverses of circulant matrices with entries in the first row of those matrices in any formation of a sequence of numbers. The main method of our study is exploiting the circulant property of the matrix and associating it with cyclic group theory to get the results of the formulation. In every discussion of those concepts, we also present some computation remarks. 
Deteksi dan Identifikasi Pelaku Kecurangan Skema Pembagian Rahasia Linear Berbasis Skema Shamir Zulkaidah Nur Ahzan; Sugi Guritman; Bib Paruhum Silalahi
Jurnal Karya Pendidikan Matematika Vol 7, No 1 (2020): Jurnal Karya Pendidikan Matematika Volume 7 Nomor 1 Tahun 2020
Publisher : Universitas Muhammadiyah Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (288.126 KB) | DOI: 10.26714/jkpm.7.1.2020.27-41

Abstract

The method that can be used to maintain security of secret in the form of cryptographic keys is by using secret sharing scheme (SSS). This method is first proposed by Adi Shamir in 1979, where the proposed scheme is a (k, n) threshold scheme. Shamir scheme is a perfect scheme under the assumption that all shareholders present their original share. However, if there are dishonest shareholders who present faked shares then the honest shareholders get nothing but a faked secret. Secret sharing scheme based on linear scheme is a scheme that can detect and identify cheaters who submit faked shares at the secret reconstruction. Detectability of this scheme when  and identifiability when  under the assumption that all shareholders present their shares randomly. After conducting a security analysis of the proposed scheme, it is obtained that to succeed in attack with cheaters who work together to fool honest shareholders then a new polynomial g(x) such that g(1) = , g(2) = , …, g(k - 1) =  and a new detector that has the same value as detector d are needed.
PENGEMBANGAN SISTEM E-VOTING DENGAN PROTOKOL TWO CENTRAL FACILITIES MENGGUNAKAN FINGERPRINT SEBAGAI OTENTIKASI VOTER Muhammad Ilyas Sikki; Sugi Guritman; Hendra Rahmawan
JREC (Journal of Electrical and Electronics) Vol. 1 No. 3 (2013): JREC (Journal of Electrical and Electronics)
Publisher : Program Studi Teknik Elektro Fakultas Teknik Universitas Islam 45 Bekasi

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The e-voting system which developed using two central facilities protokol consist of three component that is voting machine as client for interaction with voter, central legitimization agency (CLA) as server voter authentication, and central tabulating facility (CTF) as server for result recapitulation voter vote count. Research in this thesis just focused to voter authentication process on voting machine toward database of voter that stored in CLA with using fingerprint biometric technology. Fingerprint biometric technology used for voter registration process, voter verification process, and voter authentication process who will doing election. Registration process for acquire voter fingerprint image database, verification process to be sure voter database can be verificated or not, and authentication process for voter authorization who can be permitted or not by system give of vote in election
Explicit Determinant and Inverse Formulas of Skew Circulant Matrices with Alternating Fibonacci Numbers Sapto Mukti Handoyo; Sugi Guritman; Teduh Wulandari Mas'oed; Jaharuddin Jaharuddin
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32358

Abstract

Skew circulant matrices have various applications such as cryptography, signal processing, and many more. Their structure can potentially simplify their determinant and inverse computations. This study presents explicit formulas for the determinant and inverse of skew circulant matrices with entries from the alternating Fibonacci sequence. Elementary row and column operations are used to derive simple explicit formulas for the determinant and inverse. Computational tests using Wolfram Mathematica show that the algorithm built from these explicit formulas performs with much faster execution time than the built-in functions, especially for large matrix size. The proposed approach offers a practical method for the numerical computation of the determinant and inverse of these matrices
Co-Authors AHMADI Azhari, Mirza Farhan Berlian Setiawaty Bib Paruhum Silalahi Darmawan, Azhar Janjang Ekaputri, Dhea Endang Purnama Giri Fitrah Satrya Fajar Kusumah Hendra Rahmawan Hendra Rahmawan Heru Sukoco Jaharuddin Jaharuddin Khoerul Fatihin Lindayati Lindayati Lindayati Lindayati Mirza Farhan Azhari Mu'min, Ulil Albab Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Ilyas Sikki Muhammad Taufik Abdillah Nur Aliatiningtyas Nur Aliatiningtyas Pizaini Pizaini Prapto Tri Suprio Prapto Tri Suprio Prapto Tri Supriyo Rafika Husnia Munfa'ati Retno Nugroho Whidhiasih Retno Nugroho Whidhiasih Sapto Mukti Handoyo Saputra, T Murdani Shelvie Nidya Neyman Siswandi Siswandi Siswandi Siswandi TEDUH WULANDARI Teduh Wulandari Mas'oed Zulkaidah Nur Ahzan