Matrix-Based Computation in Informatics: A Conceptual Review of Linear Algebra Applications

Abstract

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.