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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi SITEKIN: Jurnal Sains, Teknologi dan Industri Jurnal Sains Matematika dan Statistika JURNAL ILMIAH MATEMATIKA DAN TERAPAN Seminar Nasional Teknologi Informasi Komunikasi dan Industri BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Zeta - Math Journal Journal of Fundamental Mathematics and Applications (JFMA) Lattice Journal : Journal of Mathematics Education and Applied CONSEN: Indonesian Journal of Community Services and Engagement Jurnal Matematika Integratif Jurnal Manajemen dan Administrasi Antartika Journal of Research on Community Engagement
Fitri Aryani
Universitas Islam Negeri Sultan Syarif Kasim Riau
Religion Humanities Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Environmental Science Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Invers Matriks RLPrFrLcirc (0,…,0,a,a) Ordo n×n Dengan n≥3 Menggunakan Matriks Blok 2×2 Rahma, Ade Novia; Asyura Nurislam, Asyura; Aryani, Fitri; Marzuki, Corry Corazon
Jurnal Sains Matematika dan Statistika Vol 11, No 2 (2025): JSMS Juli 2025
Publisher : Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/jsms.v11i2.28648

Abstract

 [1]        H. Anton dan C. Rorres, Aljabar Linear Elementer edisi kedelapan. 2004. [2]        B. J. Olson, S. W. Shaw, C. Shi, C. Pierre, dan R. G. Parker, “Circulant matrices and their application to vibration analysis,” Applied Mechanics Reviews, vol. 66, no. 4, 2014. [3]        Lin Jiang Z, Ben Xu Z, "Efficient Alghorithm For Finding The Inverse And The Group Inverse of FLS r-Circulant Matrix", J. Appl. Math & Computing, vol 18, no. 1-2, hal. 45-47, 2005. [4]        Pan, Xue dan Qin, Mei, "The Discriminance for FLDcircr Matrices and the Fast Alghorithm of Their Invers and Generalized Inverse", vol. 05, hal. 54-61, Shanghai, 2015. [5]        Jiang, Xiaoyu dan Hong, Kicheon, "Exact Determinants of some Special Circulant Matrices Involving Four Kinds of Famous Numbers", Hindawi Publishing Corporation Abstract and Applied Analysist, hal. 1-12, 2014. [6]        T. Xu, Z. Jiang, dan Z. Jiang, “Explicit Determinants of the RFPrLrR Circulant and RLPrFrL Circulant Matrices Involving Some Famous Numbers,” in Abstract and Applied Analysis, 2014, vol. 2014.  [7]        R. Rahmawati, N. Fitri, dan A. N. Rahma, “Invers Matriks RSFPLRcircfr ,” Jurnal Sains Matematika dan Statistika, vol. 6, no. 1, hal. 113–121, 2020. [8]        Z. Hasanah, Y. Muda, F. Aryani, dan C. C. Marzuki, “Determinan Dan Invers Matriks Blok  Dalam Aplikasi Matriks FLScircr Bentuk Khusus,” Seminar Nasional Teknologi Informasi, Komunikasi dan Industri (SNTIKI) 11, 2019. [9]        A. N. Rahma, M. Anggelina, dan R. Rahmawati, “Invers Matriks Blok Dalam Aplikasi Matriks FLDcircr Bentuk Khusus,” Seminar Nasional Teknologi Informasi Komunikasi dan Industri, hal. 334–344, 2019. [10]      R. Edrian, “Invers Matriks RSLPFLcircfr Bentuk Khusus  Berordo  Dengan  Menggunakan Matriks Blok  Universitas Islam Negeri Sultan Syarif Kasim Riau, 2022. [11]      H. Fikri, “Invers Matriks RFPLRcircfr Bentuk Khusus  Berordo  Dengan  Menggunakan Matriks Blok  Universitas Islam Negeri Sultan Syarif Kasim Riau, 2022. [12]     E. Rainarli, M. Si, K. E. Dewi, M.Si, and J. T. Informatika, Aljabar Linear dan Matriks. 2011. [13]      A. Yulian, S.L.M Sitio, S.D.Y. Kusuma, and P. Rosyani, Aljabar Linear dan Matriks, no. 1. 2019. [14]      Davis, Philip J., Circulan Matrices: Division of Applied Mathematics Brown University New York. 1979. [15]      Ilhamsyah, Helmi, dan F. Fran, “Determinan Dan Invers Matriks Blok ," Bimaster: Buletin Ilmiah Matematika, Statistika dan Terapannya, vol. 6, no. 03. [16]      M. Redivo-Zaglia, “Pseudo-Schur complements and their properties,” Applied numerical mathematics, vol. 50, no. 3–4, hal. 511–519, 2004. [17]     T.-T. Lu dan S.-H. Shiou, “Inverses of 2× 2 block matrices,” Computers & Mathematics with Applications, vol. 43, no. 1–2, hal. 119–129, 2002.     
TRACE OF THE ADJACENCY MATRIX n×n OF THE CYCLE GRAPH TO THE POWER OF TWO TO FIVE Aryani, Fitri; Puspita, Dian Ayu; Marzuki, Corry Corazon; Muda, Yuslenita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (548.147 KB) | DOI: 10.30598/barekengvol16iss2pp393-408

Abstract

The main aim of this research is to find the formula of the trace of adjacency matrix from a cycle graph to the power of two to five. To obtain the general form, the first step is finding the general formula of the adjacency matrix from a cycle graph to the power of two to five. Furthermore, the formula of the trace of adjacency matrix which is mentioned above obtained and proven by direct proof. We also present an implementation of the formula which is given by an example.
Trace of the Adjacency Matrix of the Star Graph and Complete Bipartite Graph Raised to a Positive Integer Power Marzuki, Corry Corazon; Aryani, Fitri; Basriati, Sri; Muda, Yuslenita
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.34255

Abstract

This research aims to derive the general form of the trace matrix of adjacency from star graphs and complete bipartite graphs with size n × n and raised to a positive integer power. To obtain the general form of the trace matrix of adjacency for these graphs, we first derive the general form of the adjacency matrix raised to a positive integer power for each given graph. The general form 14 of matrix exponentiation is proven using mathematical induction. The trace matrix of adjacency for each graph raised to a positive integer power is obtained through a direct proof based on the definition of the trace matrix. Additionally, applications of the trace matrix of adjacency from star graphs and complete bipartite graphs with size n × n and raised to a positive integer power are provided in the form of examples.
Perpangkatan dan Trace Matriks Segitiga 3 x 3 Berpangkat Bilangan Bulat Aryani, Fitri; wibowo, sundari; Marzuki, Corry Corazon; zukrianto, Zukrianto
SITEKIN: Jurnal Sains, Teknologi dan Industri Vol 19, No 2 (2022): Juni 2022
Publisher : Fakultas Sains dan Teknologi Universitas Islam Negeri Sultan Syarif Kasim Riau

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24014/sitekin.v19i2.16791

Abstract

             Penelitian ini membahas mengenai bentuk umum perpangkatan matriks dan trace matriks dari matriks segitiga berbentuk khusus dengan ukuran 3x3 berpangkat bilangan bulat. Bentuk umum perpangkatan matriks segitiga tersebut diperolah dengan menentukan terlebih dahulu perpangkatan matriks dari pangkat dua sampai pangkat sepuluh, selanjutnya dapat diduga bentuk umum perpangkatan matriks segitiga tersebut dengan pangkat bilangan bulat positif. Pendugaannya dibuktikan dengan induksi matematika. Begitu juga untuk pangkat negatif, dimulai dari pangkat negatif satu sampai pangkat negatif sepuluh. Hasil pendugaan dibuktikan dengan aturan invers. Dengan menggunakan definisi trace matriks, diperolehlah bentuk umum trace matriks segitiga berbentuk khusus dengan ukuran 3x3 berpangkat bilangan bulat positif dan negatif. Diberikan juga contoh soal untuk kedua bentuk umum tersebut. Kata Kunci: induksi matematika, invers matriks, matriks segitiga, perpangkatan matriks, trace matriks.
Forecasting the Number of Tuberculosis Patients Using Automatic Clustering And Fuzzy Logical Relationship Method Rahmawati, Rahmawati; Sarbaini, Sarbaini; Rahma, Ade Novia; Lestari, Tri Uci; Aryani, Fitri
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.18073

Abstract

Tuberculosis is an infectious disease caused by the bacterium Mycobacterium tuberculosis bacillus, which infects the lungs and can potentially cause death.  This study aims to predict the number of tuberculosis sufferers in Kampar Regency in 2022. The method used is the automatic clustering and fuzzy logical relationship method. The data analyzed is secondary data obtained from the Kampar District Health Office from 2017 to 2021. From the results of the analysis carried out using the automatic clustering and fuzzy logical relationship method, it was obtained to forecast the number of tuberculosis patients in 2022, as many as  944 people with MAPE of 0.0882%, the accuracy of forecasting results of 99.9118%, and an increase in the number of tuberculosis sufferers from 2021 to 2022 as many as 4 people.
On the Total Vertex Irregularity Strength of Series Parallel Graph sp(m,r,3) Marzuki, Corry Corazon; Utami, Muzdhalifah Marinka; Aryani, Fitri; Elviyenti, Mona; Rahma, Ade Novia
Lattice Journal : Journal of Mathematics Education and Applied Vol. 5 No. 2 (2025): Desember 2025
Publisher : Universitas Islam Negeri Sjech M. Djamil Djambek Bukittinggi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30983/lattice.v5i2.10483

Abstract

This paper addresses the problem of determining the total vertex irregularity strength of the series-parallel graph family  for  and. The total vertex irregularity strength  of a graph  is defined as the smallest integer  such that there exists a total k-labelling  where the vertex weights  are distinct for each vertex. The graph family  is generated through repeated series and parallel compositions, with parameters and a fixed structural parameter 3. To solve this problem, we construct an explicit total labelling that ensures distinct vertex weights, providing an upper bound for . Additionally, we perform a structural analysis of the graph, which yields a matching lower bound. The results demonstrate that the total vertex irregularity strength of  is given by . This work contributes a new insight into the characterization of the total vertex irregularity strength for this specific class of graphs, providing both upper and lower bounds for .   Penelitian ini membahas permasalahan dalam menentukan nilai total ketakteraturan titik pada keluarga graf seri-paralel  untuk  dan . Nilai total ketakteraturan titik  untuk suatu graf  didefinisikan sebagai nilai minimum  sehingga terdapat pelabelan total  dengan bobot titik  yang berbeda untuk setiap titik. Keluarga graf  dibangun melalui komposisi seri dan paralel secara berulang, dengan parameter  dan parameter struktur tetap 3. Untuk menyelesaikan masalah ini, kami mengonstruksi pelabelan total eksplisit yang memastikan bobot titik saling berbeda, sehingga menghasilkan batas atas untuk . Selain itu, kami melakukan analisis struktur graf untuk memperoleh batas bawah yang sesuai. Hasil penelitian ini menunjukkan bahwa total vertex irregularity strength untuk  diberikan oleh . Penelitian ini memberikan kontribusi berupa wawasan baru dalam karakterisasi nilai total ketakteraturan titik untuk kelas graf ini, dengan menyediakan batas atas dan batas bawah untuk
Invers Matriks Hankel Bentuk Khusus Ordo (n+1)×(n+1) Menggunakan Metode Adjoin Aryani, Fitri; Virginia, Jeanette Angelica Risci; Muda, Yuslenita; Rahma, Ade Novia; Marzuki, Corry Corazon
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.67254.259-270

Abstract

ABSTRAKArtikel ini bertujuan untuk menentukan bentuk umum invers Matriks Hankel berbentuk khusus  dengan menggunakan metode Adjoin. Bentuk umum invers matriks menggunakan metode adjoin diperlukan dua hal, yang pertama bentuk umum determinan Matriks Hankel dan kedua bentuk umum matriks kofaktor dari Matriks Hankel tersebut. Bentuk umum determinan Matriks Hankel diperoleh dengan memperhatikan pola determinan matriks  sampai  dan dibuktikan menggunakan induksi matematika. Bentuk umum matriks kofaktor dioperoleh dengan memperhatikan pola matriks kofaktor  sampai  dan dibuktikan  menggunakan pembuktian langsung. Lebih lanjut bentuk umum invers matriks dipresentasikan dengan menggunakan beberapa contoh soal. Kata Kunci : Determinan, Invers, Matriks Hankel, Matriks Kofaktor, Metode Adjoin.  ABSTRACTThis article aims to determine the general form of the inverse of a specially structured Hankel matrix using the Adjoint method. To derive the general form of the inverse matrix using the adjoint method, two components are required: first, the general form of the determinant of the Hankel matrix, and second, the general form of the cofactor matrix of the Hankel matrix. The general form of the determinant of the Hankel matrix is obtained by observing the determinant patterns of matrices  to  and is proven using mathematical induction. The general form of the cofactor matrix is derived by analyzing the cofactor matrix patterns of  to and is proven using direct proof. Furthermore, the general form of the inverse matrix is presented using several example problems. Keywords :  Adjoin Method,  Cofactor Matrix, Determinant, Hankel Matrix , Invers.  
Co-Authors Abdussakir Abdussakir Ade Novia Rahma Aryati Citra Asyura Nurislam, Asyura Azzahra, Frista Bella Safira Corry Corazon Marzuki Dewi Yulianti Elviyenti, Mona Hanita Hanita Hardiyanti, Aini Tina Irma Suryani Irma Suryani Jauza, Siti Mardhiyah Laraza Laraza Leni Tri Lestari Lestari, Tri Uci Lusi Andari Lutfiatul Ikromah M Eka Karnain Marhulam Marhulam Mila Sari Muhammad Rivai Muhammad Solihin Novia Arda Putri Nurul Husna Oriza Sandriani Puspita, Dian Ayu Rahmawati Rahmawati, Rahmawati Resi Arisanti Rika Taslim Rio Andesta Rosi Azwanti Dwi Maisyitah Sarbaini Sarbaini Sri . Handayani Sri Basriati Sri Handayani Sucipto, Rakhmat Hadi Tika Rizkiani Tri Novita Sari Utami, Muzdhalifah Marinka Virginia, Jeanette Angelica Risci Wati, Fitri Ambar wibowo, sundari Yulianis Yulianis Yuslenita Muda Yuslenita Muda Yuslenita Muda Yusnita Sari Zukrianto, Zukrianto Zulfa Hasanah