Matrix-Based Computation in Informatics: A Conceptual Review of Linear Algebra Applications
DOI:
https://doi.org/10.69533/4p5h1v72Keywords:
Linear Equation, Linear Space, N-Tuples, Matrix and Linear AlgebraAbstract
Linear algebra and matrices play a critical role in informatics, especially in understanding multidimensional data and computational processes. This study aims to explore the fundamental concepts and practical applications of linear algebra and matrices using a descriptive qualitative method with a literature review approach. Data sources include textbooks, international journals, and recent academic articles. The findings reveal that concepts such as vector spaces, determinants, eigenvalues, and matrix transformations are widely applied in machine learning, image processing, and modern data analysis. Techniques like Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) are proven effective for dimensionality reduction and feature extraction. The study concludes that linear algebra acts as a bridge between mathematical theory and informatics applications, serving as a foundation for developing intelligent systems and algorithms. This research is expected to serve as a conceptual reference for students and scholars in the field of information technology.
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References
Ferrerios, J. (2020). Gauss and the Mathematical Background to Stardardisation. HoST-Journal of History of Science and Technology, 14(1), 32-51.
Ghojogh Benyamin, C. M. (2023). Eigenvalue Problems in Modern Statistics. Pattern Recognition, 135, 109-125.
Golub Gene H, V. L. (2021). Matrix Computations (5th Edition). Johns Hopkins University Press.
Handayani, I. (2022). nalisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Aljabar Linear dan Matriks pada Materi Sistem Persamaan Linear. Jurnal Pendidikan Glasser.
Hanson, R. (1982). Integer Matrices Whose Inverses Contain Only Integers. The Two-Year, 13(1), 18-21.
Hatoguan, I. P., & Karo Karo, I. M. (2025). KAJIAN KONSEPTUAL MATRIKS SEBAGAI STRUKTUR DASAR DALAM ALJABAR LINEAR. JATI (Jurnal Mahasiswa Teknik Informatika), 9 (3), 5325-5329.
Hermawan, D. K. (2021). Aplikasi Vektor dan Matriks dalam Pemrosesan Data Multivariat. Jurnal Matematika dan Aplikasinya, 19(2), 89-102.
Hidayat, T. (2023). Komputasi Matriks dengan Python. Semarang: UNDIP Press.
Jolliffe Ian T, T. N. (2023). Modified PCA for High-Dimensional Data. Journal of Multivariate Analysis, 185, 104-118.
KAJIAN KONSEPTUAL MATRIKS SEBAGAI STRUKTUR DASAR DALAM ALJABAR LINEAR . (n.d.).
Kusnendi, S. (2022). Pemodelan Persamaan Struktural dengan Pendekatan Matriks. Jurnal Penelitian Bisnis, 18(1), 77-92.
Mehta Pankaj, S. D. (2022). High-Dimensional Data Analysis with Linear Algebra. Nature Reviews Physics, 4(6), 403-418.
Murphy, K. P. (2022). Probabilistic Machine Learning: Advanced Topics. MIT Press, Chapter 20: Linear Algebra.
Noviana, W. (2023). Matriks dan Transformasi Linear. Surabaya: Unesa Press.
Rathee, S. (2023). A Study on Linear Algebra and it's Significance. International Journal of Engineering, Science and Mathematics, 12(1), 91-99.
Rizal, M. (2023.). Aljabar Linear untuk Optimasi Rute. J. Mat. UNJ, 6(2), 45-53.
Spurio, M. (2023). Vectors and Operations of Matrix . In The Fundamentals of Newtonian Mechanics: For an Introductory Approach to Modern Physics, 27-46.
Widodo, C. S. (2022). Analisis Kinerja Algoritma SVD untuk Reduksi Dimensi Data. Media Statistika, 14(1), 33-47.
Wulantina, E. (2022). Pengembangan E-Modul Aljabar Linear Dengan Pendekatan Pendidikan Matematika Realistik Berbasis Nilai-Nilai Keislaman. JNPM (JurnalNasional Pendidikan Matematika).
Zhang Annie, L. W. (2022). Randomized Linear Algebra for Big Data Applications. IEEE Transactions on Knowledge and Data Engineering, 34(5), 2103-2116.
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Copyright (c) 2025 Muhammad Nazar Aufa Nazar, Diny Syarifah Sany Diny (Author)
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